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Lower Bounds for Cubic Optimization over the Sphere J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-15 Christoph Buchheim, Marcia Fampa, Orlando Sarmiento
We consider the problem of minimizing a polynomial function of degree three over the boundary of the sphere. If the objective is quadratic instead of cubic, this is the well-studied trust region subproblem, which is known to be tractable. In the cubic case, the problem turns out to be NP-hard. In this paper, we derive and evaluate different approaches for computing lower bounds for the cubic problem
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An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-13 Bennet Gebken, Sebastian Peitz
We present an efficient descent method for unconstrained, locally Lipschitz multiobjective optimization problems. The method is realized by combining a theoretical result regarding the computation of descent directions for nonsmooth multiobjective optimization problems with a practical method to approximate the subdifferentials of the objective functions. We show convergence to points which satisfy
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New Results on Superlinear Convergence of Classical Quasi-Newton Methods J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-09 Anton Rodomanov, Yurii Nesterov
We present a new theoretical analysis of local superlinear convergence of classical quasi-Newton methods from the convex Broyden class. As a result, we obtain a significant improvement in the currently known estimates of the convergence rates for these methods. In particular, we show that the corresponding rate of the Broyden–Fletcher–Goldfarb–Shanno method depends only on the product of the dimensionality
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A Unified Convergence Analysis of Stochastic Bregman Proximal Gradient and Extragradient Methods J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-08 Xiantao Xiao
We consider a mini-batch stochastic Bregman proximal gradient method and a mini-batch stochastic Bregman proximal extragradient method for stochastic convex composite optimization problems. A simplified and unified convergence analysis framework is proposed to obtain almost sure convergence properties and expected convergence rates of the mini-batch stochastic Bregman proximal gradient method and its
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Characterizing Existence of Minimizers and Optimality to Nonconvex Quadratic Integrals J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-08 Fabián Flores-Bazán, Luis González-Valencia
Quadratic functions play an important role in applied mathematics. In this paper, we consider the problem of minimizing the integral of a (not necessarily convex) quadratic function in a bounded subset of nonnegative integrable functions defined on a finite-dimensional space that is not compact with respect to any (locally convex) topology in the space of integrable functions. We establish a complete
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Well-Posedness of Minimization Problems in Contact Mechanics J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-08 Mircea Sofonea, Yi-bin Xiao
We consider an abstract minimization problem in reflexive Banach spaces together with a specific family of approximating sets, constructed by perturbing the cost functional and the set of constraints. For this problem, we state and prove various well-posedness results in the sense of Tykhonov, under different assumptions on the data. The proofs are based on arguments of lower semicontinuity, compactness
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Strong Convergence Theorems for Solving Variational Inequality Problems with Pseudo-monotone and Non-Lipschitz Operators J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-08 Gang Cai, Qiao-Li Dong, Yu Peng
In this paper, we propose a new viscosity extragradient algorithm for solving variational inequality problems of pseudo-monotone and non-Lipschitz continuous operator in real Hilbert spaces. We prove a strong convergence theorem under some appropriate conditions imposed on the parameters. Finally, we give some numerical experiments to illustrate the advantages of our proposed algorithms. The main results
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Optimal Economic Growth Models with Nonlinear Utility Functions J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-08 Vu Thi Huong, Jen-Chih Yao, Nguyen Dong Yen
We study a class of finite horizon optimal economic growth problems with nonlinear utility functions and linear production functions. By using a maximum principle in the optimal control theory and employing the special structure of the problems, we are able to explicitly describe the unique solution via input parameters. Economic interpretations of the obtained results and an open problem about the
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Convexification Method for Bilevel Programs with a Nonconvex Follower’s Problem J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-08 Gaoxi Li, Xinmin Yang
A new numerical method is presented for bilevel programs with a nonconvex follower’s problem. The basic idea is to piecewise construct convex relaxations of the follower’s problems, replace the relaxed follower’s problems equivalently by their Karush–Kuhn–Tucker conditions and solve the resulting mathematical programs with equilibrium constraints. The convex relaxations and needed parameters are constructed
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Topologies for the Continuous Representability of All Continuous Total Preorders J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-08 Gianni Bosi, Magalì Zuanon
In this paper, we present a new simple axiomatization of useful topologies, i.e., topologies on an arbitrary set, with respect to which every continuous total preorder admits a continuous utility representation. In particular, we show that, for completely regular spaces, a topology is useful, if and only if it is separable, and every isolated chain of open and closed sets is countable. As a specific
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Global Regularity for Minimizers of Some Anisotropic Variational Integrals J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-08 Hongya Gao, Miaomiao Huang, Wei Ren
We give regularity results for minimizers of two special cases of polyconvex functionals. Under some structural assumptions on the energy density, we prove that minimizers are either bounded, or have suitable integrability properties, by using the classical Stampacchia Lemma.
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Algorithms and Complexity for a Class of Combinatorial Optimization Problems with Labelling J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-08 Zishen Yang, Wei Wang, Majun Shi
In this paper, we propose to study a wide class of combinatorial optimization problems called combinatorial optimization problems with labelling. First, we give a combinatorial method to deal with the labelling version of some classical combinatorial optimization problems including minimum vertex cover, maximum independent set, minimum dominating set and minimum set cover, and convert the labelling
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Extended Sufficient Conditions for Strong Minimality in the Bolza Problem: Applications to Space Trajectory Optimization J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-08 Leonardo Mazzini
This paper expands the existing sufficiency results for the strong minimality of an extremal of the Bolza problem. We cover the case where the strict Legendre Clebsh conditions are not strictly verified. An efficient, easy to use, algorithm to prove minimality is provided. It can be used on solutions with bang-bang control and does not require any local controllability property. The interval where
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An Extragradient Method for Solving Variational Inequalities without Monotonicity J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-08 Ming Lei, Yiran He
A new extragradient projection method, which does not require generalized monotonicity, is devised in this paper. In order to ensure its global convergence, we assume only that the Minty variational inequality has a solution. In particular, it applies to quasimonotone variational inequalities having a nontrivial solution.
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A Nonmonotone Trust Region Method for Unconstrained Optimization Problems on Riemannian Manifolds J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-08 Xiaobo Li, Xianfu Wang, Manish Krishan Lal
We propose a nonmonotone trust region method for unconstrained optimization problems on Riemannian manifolds. Global convergence to the first-order stationary points is proved under some reasonable conditions. We also establish local R-linear, super-linear and quadratic convergence rates. Preliminary experiments show that the algorithm is efficient.
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Diffeomorphic Shape Matching by Operator Splitting in 3D Cardiology Imaging J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-05 Peng Zhang, Andreas Mang, Jiwen He, Robert Azencott, K. Carlos El-Tallawi, William A. Zoghbi
We develop an operator splitting approach to solve diffeomorphic matching problems for sequences of surfaces in three-dimensional space. The goal is to smoothly match, at very fast rate, finite sequences of observed 3D-snapshots extracted from movies recording the smooth dynamic deformations of “soft” surfaces. We have implemented our algorithms in a proprietary software installed at The Methodist
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Local Linear Convergence of the Alternating Direction Method of Multipliers for Nonconvex Separable Optimization Problems J. Optim. Theory Appl. (IF 1.388) Pub Date : 2021-01-04 Zehui Jia, Xue Gao, Xingju Cai, Deren Han
In this paper, we consider the convergence rate of the alternating direction method of multipliers for solving the nonconvex separable optimization problems. Based on the error bound condition, we prove that the sequence generated by the alternating direction method of multipliers converges locally to a critical point of the nonconvex optimization problem in a linear convergence rate, and the corresponding
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Convergent Inexact Penalty Decomposition Methods for Cardinality-Constrained Problems J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-12-14 Matteo Lapucci, Tommaso Levato, Marco Sciandrone
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On the Linear Convergence of Forward–Backward Splitting Method: Part I—Convergence Analysis J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-11-28 Yunier Bello-Cruz, Guoyin Li, Tran T. A. Nghia
In this paper, we study the complexity of the forward–backward splitting method with Beck–Teboulle’s line search for solving convex optimization problems, where the objective function can be split into the sum of a differentiable function and a nonsmooth function. We show that the method converges weakly to an optimal solution in Hilbert spaces, under mild standing assumptions without the global Lipschitz
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Trade-Off Ratio Functions for Linear and Piecewise Linear Multi-objective Optimization Problems J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-11-28 Siming Pan, Shaokai Lu, Kaiwen Meng, Shengkun Zhu
In this paper, we introduce the concept of trade-off ratio function, which is closely related to the well-known Geoffrion’s proper efficiency for multi-objective optimization problems, and investigate its boundedness property. For linear multi-objective optimization problems, we show that the trade-off ratio function is bounded on the efficient solution set. For piecewise linear multi-objective optimization
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Static Upper/Lower Thrust and Kinematic Work Balance Stationarity for Least-Thickness Circular Masonry Arch Optimization J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-11-28 Giuseppe Cocchetti, Egidio Rizzi
This paper re-considers a recent analysis on the so-called Couplet–Heyman problem of least-thickness circular masonry arch structural form optimization and provides complementary and novel information and perspectives, specifically in terms of the optimization problem, and its implications in the general understanding of the Mechanics (statics) of masonry arches. First, typical underlying solutions
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The Generalized Minimum Branch Vertices Problem: Properties and Polyhedral Analysis J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-11-27 Francesco Carrabs, Raffaele Cerulli, Ciriaco D’Ambrosio, Federica Laureana
This article introduces the Generalized Minimum Branch Vertices problem. Given an undirected graph, where the set of vertices is partitioned into clusters, the Generalized Minimum Branch Vertices problem consists of finding a tree spanning exactly one vertex for each cluster and having the minimum number of branch vertices, namely vertices with degree greater than two. When each cluster is a singleton
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Accelerated Diagonal Steepest Descent Method for Unconstrained Multiobjective Optimization J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-11-23 Mustapha El Moudden, Abdelkrim El Mouatasim
In this paper, we propose two methods for solving unconstrained multiobjective optimization problems. First, we present a diagonal steepest descent method, in which, at each iteration, a common diagonal matrix is used to approximate the Hessian of every objective function. This method works directly with the objective functions, without using any kind of a priori chosen parameters. It is proved that
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Kurdyka–Łojasiewicz Property of Zero-Norm Composite Functions J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-11-23 Yuqia Wu, Shaohua Pan, Shujun Bi
This paper focuses on a class of zero-norm composite optimization problems. For this class of nonconvex nonsmooth problems, we establish the Kurdyka–Łojasiewicz property of exponent being a half for its objective function under a suitable assumption and provide some examples to illustrate that such an assumption is not very restricted which, in particular, involve the zero-norm regularized or constrained
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Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective Optimization J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-11-23 Ana Luísa Custódio, Youssef Diouane, Rohollah Garmanjani, Elisa Riccietti
Direct Multisearch is a well-established class of algorithms, suited for multiobjective derivative-free optimization. In this work, we analyze the worst-case complexity of this class of methods in its most general formulation for unconstrained optimization. Considering nonconvex smooth functions, we show that to drive a given criticality measure below a specific positive threshold, Direct Multisearch
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Long-Time Behavior of a Gradient System Governed by a Quasiconvex Function J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-11-21 Mohsen Rahimi Piranfar, Hadi Khatibzadeh
We consider a second-order differential equation governed by a quasiconvex function with a nonempty set of minimizers. Assuming that the gradient of this function is Lipschitz continuous, the existence of solutions to the gradient system is guaranteed. We study the asymptotic behavior of these solutions in continuous and discrete times. More precisely, we show that, if a solution is bounded, then it
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Perturbation Analysis of Singular Semidefinite Programs and Its Applications to Control Problems J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-11-18 Yoshiyuki Sekiguchi, Hayato Waki
We consider sensitivity of a semidefinite program under perturbations in the case that the primal problem is strictly feasible and the dual problem is weakly feasible. When the coefficient matrices are perturbed, the optimal values can change discontinuously as explained in concrete examples. We show that the optimal value of such a semidefinite program changes continuously under conditions involving
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Stochastic Multi-objective Optimisation of Exoskeleton Structures J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-11-18 Anna Reggio, Rita Greco, Giuseppe Carlo Marano, Giuseppe Andrea Ferro
In this study, a structural optimisation problem, addressed through a stochastic multi-objective approach, is formulated and solved. The problem deals with the optimal design of exoskeleton structures, conceived as vibration control systems under seismic loading. The exoskeleton structure is assumed to be coupled to an existing primary inner structure for seismic retrofit: the aim is to limit the dynamic
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Variational Inequality Type Formulations of General Market Equilibrium Problems with Local Information J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-11-17 Igor Konnov
We suggest a new approach to creation of general market equilibrium models involving economic agents with local and partial knowledge about the system and under different restrictions. The market equilibrium problem is then formulated as a quasi-variational inequality that enables us to establish existence results for the model in different settings. We also describe dynamic processes, which fall into
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A Second-Order Sufficient Optimality Condition for Risk-Neutral Bi-level Stochastic Linear Programs J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-11-10 Matthias Claus
The expectation functionals, which arise in risk-neutral bi-level stochastic linear models with random lower-level right-hand side, are known to be continuously differentiable, if the underlying probability measure has a Lebesgue density. We show that the gradient may fail to be local Lipschitz continuous under this assumption. Our main result provides sufficient conditions for Lipschitz continuity
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Stability of Gated Recurrent Unit Neural Networks: Convex Combination Formulation Approach J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-11-05 Dušan M. Stipanović, Mirna N. Kapetina, Milan R. Rapaić, Boris Murmann
In this paper, a particular discrete-time nonlinear and time-invariant system represented as a vector difference equation is analyzed for its stability properties. The motivation for analyzing this particular system is that it models gated recurrent unit neural networks commonly used and well known in machine learning applications. From the technical perspective, the analyses exploit the systems similarities
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Acceptable Solutions and Backward Errors for Tensor Complementarity Problems J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-11-03 Shouqiang Du, Weiyang Ding, Yimin Wei
Backward error analysis reveals the numerical stability of algorithms and provides elaborate stopping criteria for iterative methods. Compared with numerical linear algebra problems, the backward error analysis for optimization problems is more rarely conducted in the literature. This paper is devoted to the backward error analysis for several generalizations of tensor complementarity problems. We
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On Relatively Solid Convex Cones in Real Linear Spaces J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-31 Vicente Novo, Constantin Zălinescu
Having a convex cone K in an infinite-dimensional real linear space X, Adán and Novo stated (in J Optim Theory Appl 121:515–540, 2004) that the relative algebraic interior of K is nonempty if and only if the relative algebraic interior of the positive dual cone of K is nonempty. In this paper, we show that the direct implication is not true even if K is closed with respect to the finest locally convex
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Optimizing the Efficiency of First-Order Methods for Decreasing the Gradient of Smooth Convex Functions J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-30 Donghwan Kim, Jeffrey A. Fessler
This paper optimizes the step coefficients of first-order methods for smooth convex minimization in terms of the worst-case convergence bound (i.e., efficiency) of the decrease in the gradient norm. This work is based on the performance estimation problem approach. The worst-case gradient bound of the resulting method is optimal up to a constant for large-dimensional smooth convex minimization problems
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Measure-Driven Nonlinear Dynamic Systems with Applications to Optimal Impulsive Controls J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-28 Nasir Uddin Ahmed, Shian Wang
In this paper, we consider a class of nonlinear systems driven by measures generalizing the class of impulsive systems. We use measures as control and prove existence of optimal controls (measures) and present necessary conditions of optimality. We apply the general results to derive necessary conditions of optimality for purely impulse-driven systems. These results are then applied to optimal control
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Quantization for Uniform Distributions on Hexagonal, Semicircular, and Elliptical Curves J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-24 Gabriela Pena, Hansapani Rodrigo, Mrinal Kanti Roychowdhury, Josef Sifuentes, Erwin Suazo
In this paper, first we have defined a uniform distribution on the boundary of a regular hexagon and then investigate the optimal sets of n-means and the nth quantization errors for all positive integers n. We give an exact formula to determine them, if n is of the form \(n=6k\) for some positive integer k. We further calculate the quantization dimension, the quantization coefficient, and show that
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Is a Finite Intersection of Balls Covered by a Finite Union of Balls in Euclidean Spaces? J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-24 Vincent Runge
Considering a finite intersection of balls and a finite union of other balls in an Euclidean space, we propose an exact method to test whether the intersection is covered by the union. We reformulate this problem into quadratic programming problems. For each problem, we study the intersection between a sphere and a Voronoi-like polyhedron. That way, we get information about a possible overlap between
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Nash Equilibrium Seeking in Quadratic Noncooperative Games Under Two Delayed Information-Sharing Schemes J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-23 Tiago Roux Oliveira, Victor Hugo Pereira Rodrigues, Miroslav Krstić, Tamer Başar
In this paper, we propose non-model-based strategies for locally stable convergence to Nash equilibrium in quadratic noncooperative games where acquisition of information (of two different types) incurs delays. Two sets of results are introduced: (a) one, which we call cooperative scenario, where each player employs the knowledge of the functional form of his payoff and knowledge of other players’
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Representation of Weak Solutions of Convex Hamilton–Jacobi–Bellman Equations on Infinite Horizon J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-23 Vincenzo Basco
In the present paper, it is provided a representation result for the weak solutions of a class of evolutionary Hamilton–Jacobi–Bellman equations on infinite horizon, with Hamiltonians measurable in time and fiber convex. Such Hamiltonians are associated with a—faithful—representation, namely involving two functions measurable in time and locally Lipschitz in the state and control. Our results concern
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Projections onto the Intersection of a One-Norm Ball or Sphere and a Two-Norm Ball or Sphere J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-21 Hongying Liu, Hao Wang, Mengmeng Song
This paper focuses on designing a unified approach for computing the projection onto the intersection of a one-norm ball or sphere and a two-norm ball or sphere. We show that the solutions of these problems can all be determined by the root of the same piecewise quadratic function. We make use of the special structure of the auxiliary function and propose a novel bisection algorithm with finite termination
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On the Extension of Continuous Quasiconvex Functions J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-20 Carlo Alberto De Bernardi
We study the problem of extending continuous quasiconvex real-valued functions from a subspace of a real normed linear space. Our results are essentially finite-dimensional and are based on a technical lemma which permits to “extend” a nested family of open convex subsets of a given subspace to a nested family of open convex sets in the whole space, in such a way that certain topological conditions
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Conditional Interior and Conditional Closure of Random Sets J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-20 Meriam El Mansour, Emmanuel Lépinette
In this paper, we introduce two new types of conditional random set taking values in a Banach space: the conditional interior and the conditional closure. The conditional interior is a version of the conditional core, as introduced by A. Truffert and recently developed by Lépinette and Molchanov, and may be seen as a measurable version of the topological interior. The conditional closure is a generalization
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An Existence Result for Quasi-equilibrium Problems via Ekeland’s Variational Principle J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-19 John Cotrina, Michel Théra, Javier Zúñiga
This paper deals with the existence of solutions to equilibrium and quasi-equilibrium problems without any convexity assumption. Coverage includes some equivalences to the Ekeland variational principle for bifunctions and basic facts about transfer lower continuity. An application is given to systems of quasi-equilibrium problems.
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Robust Feedback Control for a Linear Chain of Oscillators J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-17 Alexander Ovseevich, Igor Ananievski
We study the problem of bringing a linear chain of masses connected by springs to an equilibrium in finite time by means of a control force applied to the first mass. We describe explicitly the desired feedback control and establish its local equivalence to the minimum-time one. We prove the robustness of the control with respect to unknown disturbances and compute the time of transfer as well as its
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Optimal Sensors Placement in Dynamic Damage Detection of Beams Using a Statistical Approach J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-16 Egidio Lofrano, Marco Pingaro, Patrizia Trovalusci, Achille Paolone
Structural monitoring plays a central role in civil engineering; in particular, optimal sensor positioning is essential for correct monitoring both in terms of usable data and for optimizing the cost of the setup sensors. In this context, we focus our attention on the identification of the dynamic response of beam-like structures with uncertain damages. In particular, the non-localized damage is described
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A Frank–Wolfe-Type Theorem for Cubic Programs and Solvability for Quadratic Variational Inequalities J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-09 Tran Van Nghi, Nguyen Nang Tam
In this paper, we present a Frank–Wolfe-type theorem for nonconvex cubic programming problems. This result is a direct extension of the previous ones by Andronov et al. (Izvestija Akadem. Nauk SSSR, Tekhnicheskaja Kibernetika 4:194–197, 1982) and Flores-Bazán et al. (Math. Program. 145:263–290, 2014). Under suitable conditions, we characterize the compactness of the solution set of cubic programming
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Optimal Dividend and Capital Structure with Debt Covenants J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-09 Etienne Chevalier, Vathana Ly Vath, Alexandre Roch
We consider an optimal dividend and capital structure problem for a firm, which holds a certain amount of debt to which is associated a financial ratio covenant between the firm and its creditors. We study optimal policies under a bankruptcy framework, using a mixed reduced and structural approach in modeling default and liquidation times. Once in default, the firm is given a grace period during which
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A Discounted Approach in Communicating Average Markov Decision Chains Under Risk-Aversion J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-07 Julio Saucedo-Zul, Rolando Cavazos-Cadena, Hugo Cruz-Suárez
This work concerns with discrete-time Markov decision processes on a denumerable state space. Assuming that the decision maker is risk-averse with constant risk-sensitivity coefficient, the performance of a control policy is measured by an average criterion associated with a non-negative and bounded cost function. Under conditions ensuring that the optimal average cost is constant, but not necessarily
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Strength Optimisation of Variable Angle-Tow Composites Through a Laminate-Level Failure Criterion J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-03 Anita Catapano, Marco Montemurro
The development of additive manufacturing techniques for composite structures brought the emergence of a new class of composite materials: the variable angle-tow composites. Additive manufacturing of reinforced polymers allows the tow to be placed along a curvilinear path in each lamina. Accordingly, optimised solutions with enhanced properties can be manufactured. In this work, the multi-scale two-level
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Generalized Farkas Lemma with Adjustable Variables and Two-Stage Robust Linear Programs J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-03 Thai Doan Chuong, Vaithilingam Jeyakumar
In this paper, we establish strong duality between affinely adjustable two-stage robust linear programs and their dual semidefinite programs under a general uncertainty set, that covers most of the commonly used uncertainty sets of robust optimization. This is achieved by first deriving a new version of Farkas’ lemma for a parametric linear inequality system with affinely adjustable variables. Our
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A Constructive Approximation of Interpolating Bézier Curves on Riemannian Symmetric Spaces J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-10-03 Ines Adouani, Chafik Samir
We propose a new method to approximate curves that interpolate a given set of time-labeled data on Riemannian symmetric spaces. First, we present our new formulation on the Euclidean space as a result of minimizing the mean square acceleration. This motivates its generalization on some Riemannian symmetric manifolds. Indeed, we generalize the proposed solution to the the special orthogonal group, the
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On the Role of the Objective in the Optimization of Compartmental Models for Biomedical Therapies J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-09-30 Urszula Ledzewicz, Heinz Schättler
We review and discuss results obtained through an application of tools of nonlinear optimal control to biomedical problems. We discuss various aspects of the modeling of the dynamics (such as growth and interaction terms), modeling of treatment (including pharmacometrics of the drugs), and give special attention to the choice of the objective functional to be minimized. Indeed, many properties of optimal
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Nonzero-Sum Stochastic Differential Reinsurance Games with Jump–Diffusion Processes J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-09-30 Negash Medhin, Chuan Xu
In this paper, a nonzero-sum stochastic differential reinsurance game is studied. A model including controls for the market share (advertising), investment, and reinsurance policies is considered. A jump–diffusion process is used to represent insurance claims. Necessary conditions that would lead to the Nash equilibrium can be found in the duopoly game we consider. Cases with and without controls on
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Constraint Qualifications for Karush–Kuhn–Tucker Conditions in Multiobjective Optimization J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-09-29 Gabriel Haeser, Alberto Ramos
The notion of a normal cone of a given set is paramount in optimization and variational analysis. In this work, we give a definition of a multiobjective normal cone, which is suitable for studying optimality conditions and constraint qualifications for multiobjective optimization problems. A detailed study of the properties of the multiobjective normal cone is conducted. With this tool, we were able
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Degree Theory for Generalized Mixed Quasi-variational Inequalities and Its Applications J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-09-28 Zhong-bao Wang, Yi-bin Xiao, Zhang-you Chen
The present paper is devoted to building degree theory for a generalized mixed quasi-variational inequality in finite dimensional spaces. Then, by employing the obtained results, we prove the existence and stability of solutions to the considered generalized mixed quasi-variational inequality.
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The Engulfing Property from a Convex Analysis Viewpoint J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-09-28 Andrea Calogero, Rita Pini
In this note, we provide a simple proof of some properties enjoyed by convex functions having the engulfing property. In particular, making use only of results peculiar to convex analysis, we prove that differentiability and strict convexity are conditions intrinsic to the engulfing property.
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Existence of Solutions for Implicit Obstacle Problems of Fractional Laplacian Type Involving Set-Valued Operators J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-09-25 Dumitru Motreanu, Van Thien Nguyen, Shengda Zeng
The paper is devoted to a new kind of implicit obstacle problem given by a fractional Laplacian-type operator and a set-valued term, which is described by a generalized gradient. An existence theorem for the considered implicit obstacle problem is established, using a surjectivity theorem for set-valued mappings, Kluge’s fixed point principle and nonsmooth analysis.
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Minimax and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations for Time-Delay Systems J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-09-21 Anton Plaksin
The paper deals with a Bolza optimal control problem for a dynamical system, whose motion is described by a delay differential equation under an initial condition defined by a piecewise continuous function. For the value functional in this problem, the Cauchy problem for the Hamilton–Jacobi–Bellman equation with coinvariant derivatives is considered. Minimax and viscosity solutions of the Cauchy problem
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Minimizers of Sparsity Regularized Huber Loss Function J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-09-19 Deniz Akkaya, Mustafa Ç. Pınar
We investigate the structure of the local and global minimizers of the Huber loss function regularized with a sparsity inducing L0 norm term. We characterize local minimizers and establish conditions that are necessary and sufficient for a local minimizer to be strict. A necessary condition is established for global minimizers, as well as non-emptiness of the set of global minimizers. The sparsity
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Isotonicity of Proximity Operators in General Quasi-Lattices and Optimization Problems J. Optim. Theory Appl. (IF 1.388) Pub Date : 2020-09-18 Dezhou Kong, Lishan Liu, Yonghong Wu
Motivated by the recent works on proximity operators and isotone projection cones, in this paper, we discuss the isotonicity of the proximity operator in quasi-lattices, endowed with general cones. First, we show that Hilbert spaces, endowed with general cones, are quasi-lattices, in which the isotonicity of the proximity operator with respect to one order and two mutually dual orders is then, respectively