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Forward–Reflected–Backward Splitting Algorithms with Momentum: Weak, Linear and Strong Convergence Results J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-03-15 Yonghong Yao, Abubakar Adamu, Yekini Shehu
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Primal-Dual Algorithm for Distributed Optimization with Coupled Constraints J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-03-13 Kai Gong, Liwei Zhang
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Generalized Newton Method with Positive Definite Regularization for Nonsmooth Optimization Problems with Nonisolated Solutions J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-03-13
Abstract We propose a coderivative-based generalized regularized Newton method with positive definite regularization term (GRNM-PD) to solve \(C^{1,1}\) optimization problems. In GRNM-PD, a general positive definite symmetric matrix is used to regularize the generalized Hessian, in contrast to the recently proposed GRNM, which uses the identity matrix. Our approach features global convergence and fast
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Understanding Badly and Well-Behaved Linear Matrix Inequalities Via Semi-infinite Optimization J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-03-13 Qinghong Zhang
In this paper, we use a linear semi-infinite optimization approach to study badly and well-behaved linear matrix inequalities. We utilize a result on uniform LP duality of linear semi-infinite optimization problems to prove recent results obtained by Pataki. Such an approach not only provides alternative proofs of known results, but also gives new insights about badly and well-behaved linear matrix
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The Inexact Cyclic Block Proximal Gradient Method and Properties of Inexact Proximal Maps J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-03-13 Leandro Farias Maia, David Huckleberry Gutman, Ryan Christopher Hughes
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Differential Stability Properties of Convex Optimization and Optimal Control Problems J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-03-12 Nguyen Thi Toan, Le Quang Thuy
This paper studies the solution stability of convex optimization and discrete convex optimal control problems in Banach spaces, where the solution set may be empty. For both the optimization problem and the optimal control problem, formulas for the \(\varepsilon \)-subdifferential of the optimal value function are derived without qualification conditions. We first calculate the \(\varepsilon \)-subdifferential
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Nonsmooth Nonconvex Stochastic Heavy Ball J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-03-11 Tam Le
Motivated by the conspicuous use of momentum-based algorithms in deep learning, we study a nonsmooth nonconvex stochastic heavy ball method and show its convergence. Our approach builds upon semialgebraic (definable) assumptions commonly met in practical situations and combines a nonsmooth calculus with a differential inclusion method. Additionally, we provide general conditions for the sample distribution
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Lower Bounds on the Noiseless Worst-Case Complexity of Efficient Global Optimization J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-03-11 Wenjie Xu, Yuning Jiang, Emilio T. Maddalena, Colin N. Jones
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Distributed Dual Subgradient Methods with Averaging and Applications to Grid Optimization J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-03-08
Abstract We study finite-time performance of a recently proposed distributed dual subgradient (DDSG) method for convex-constrained multi-agent optimization problems. The algorithm enjoys performance guarantees on the last primal iterate, as opposed to those derived for ergodic means for standard DDSG algorithms. Our work improves the recently published convergence rate of \({{\mathcal {O}}}(\log T/\sqrt{T})\)
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Cardinality-Constrained Multi-objective Optimization: Novel Optimality Conditions and Algorithms J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-03-04 Matteo Lapucci, Pierluigi Mansueto
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Riemannian Interior Point Methods for Constrained Optimization on Manifolds J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-03-04 Zhijian Lai, Akiko Yoshise
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Second-Order Conditions for the Existence of Augmented Lagrange Multipliers for Sparse Optimization J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-03-02
Abstract In this paper, we consider the augmented Lagrangian duality for optimization problems with sparsity and abstract set constraints and present second-order conditions for the existence of augmented Lagrange multipliers by calculating the second-order epi-derivative of the augmented Lagrangian. The ingredient of the augmented Lagrangian here includes the indicator function of a sparse set and
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Stochastic Maximum Principle for Generalized Mean-Field Delay Control Problem J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-03-01 Hancheng Guo, Jie Xiong, Jiayu Zheng
In this paper, we first derive the existence and uniqueness theorems for solutions to a class of generalized mean-field delay stochastic differential equations and mean-field anticipated backward stochastic differential equations (MFABSDEs). Then we study the stochastic maximum principle for generalized mean-field delay control problem. Since the state equation is distribution-depending, we define
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A Universal Accelerated Primal–Dual Method for Convex Optimization Problems J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-03-01 Hao Luo
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Quadratic Growth and Linear Convergence of a DCA Method for Quartic Minimization over the Sphere J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-03-01 Shenglong Hu, Zhifang Yan
The quartic minimization over the sphere can be reformulated as a nonlinear nonconvex semidefinite program over the spectraplex. In this paper, under mild assumptions, we show that the reformulated nonlinear semidefinite program possesses the quadratic growth property at a rank one critical point which is a local minimizer of the quartic minimization problem. The quadratic growth property further implies
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Measure-Valued Optimal Control for Size-Structured Population Models with Diffusion J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-03-01 Nobuyuki Kato
We consider a control problem to maximize a profit from harvesting in agriculture or aquaculture, where the population is governed by size-structured population models with spatial diffusion. We show the existence of an optimal control of harvesting rate which is a measure with respect to size expressed by the distributional partial derivative of a function of bounded variation.
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Convergence Results for a Class of Generalized Second-Order Evolutionary Variational–Hemivariational Inequalities J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-26 Dong-ling Cai, Yi-bin Xiao
In this paper, we deal with a class of second-order evolutionary history-dependent variational–hemivariational inequalities with constraint. The unique solvability of the considered second-order evolutionary inequality problem is established via a surjectivity result combined with a fixed point theorem. Moreover, we construct a regularized problem for such second-order evolutionary history-dependent
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The Difference of Convex Algorithm on Hadamard Manifolds J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-26 Ronny Bergmann, Orizon P. Ferreira, Elianderson M. Santos, João Carlos O. Souza
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On Optimizing Ensemble Models using Column Generation J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-22 Vanya Aziz, Ouyang Wu, Ivo Nowak, Eligius M. T. Hendrix, Jan Kronqvist
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On Completely Mixed Games J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-22 Parthasarathy Thiruvankatachari, Ravindran Gomatam, Sunil Kumar
A matrix game is considered completely mixed if all the optimal pairs of strategies in the game are completely mixed. In this paper, we establish that a matrix game A, with a value of zero, is completely mixed if and only if the value of the game associated with \(A +D_i \) is positive for all i, where \(D_i\) represents a diagonal matrix where ith diagonal entry is 1 and else 0. Additionally, we address
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Compatible TOSets with POSets: An Application to Additive Manufacturing J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-21 Policarpo Abascal, Fernando Fueyo, Jorge Jiménez, Antonio Palacio, Maria Luisa Serrano
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Dynamic Programming of the Stochastic Burgers Equation Driven by Lévy Noise J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-20 Manil T. Mohan, Kumarasamy Sakthivel, Sivaguru S. Sritharan
In this work, we study the optimal control of stochastic Burgers equation perturbed by Gaussian and Lévy-type noises with distributed control process acting on the state equation. We use dynamic programming approach for the feedback synthesis to obtain an infinite-dimensional second-order Hamilton–Jacobi–Bellman (HJB) equation consisting of an integro-differential operator with Lévy measure associated
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A Mirror Inertial Forward–Reflected–Backward Splitting: Convergence Analysis Beyond Convexity and Lipschitz Smoothness J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-20 Ziyuan Wang, Andreas Themelis, Hongjia Ou, Xianfu Wang
This work investigates a Bregman and inertial extension of the forward–reflected–backward algorithm (Malitsky and Tam in SIAM J Optim 30:1451–1472, 2020) applied to structured nonconvex minimization problems under relative smoothness. To this end, the proposed algorithm hinges on two key features: taking inertial steps in the dual space, and allowing for possibly negative inertial values. The interpretation
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Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-17 Konstantin Sonntag, Sebastian Peitz
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Locally Optimal Eigenpairs of Orthogonally Decomposable Tensors: A Generalized Proof J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-17 Lei Wang, Xiurui Geng, Lei Zhang
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k-Sparse Vector Recovery via $$\ell _1-\alpha \ell _2$$ Local Minimization J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-15
Abstract This paper studies the \(\ell _1-\alpha \ell _2\) local minimization model for \(\alpha \in (0,2]\) , which is the first time to consider the case of \(\alpha >1\) . We obtain the necessary and sufficient conditions for a fixed sparse signal to be recovered from this model. Based on this condition, we also obtain the necessary and sufficient conditions for any k-sparse signal to be recovered
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Matrix Optimization Problem Involving Group Sparsity and Nonnegativity Constraints J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-12
Abstract In this paper, we consider the matrix optimization problem with group sparsity and nonnegativity constraints. We analyze the optimality conditions and develop two matrix-based improved iterative hard thresholding algorithms for the problem, using the projected gradient method with the Armijo-type stepsize rule and the fixed stepsize, respectively. We then prove that the whole sequence generated
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On the Relationship Between the Kurdyka–Łojasiewicz Property and Error Bounds on Hadamard Manifolds J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-11 João Xavier da Cruz Neto, Ítalo Dowell Lira Melo, Paulo Alexandre Sousa, João Carlos de Oliveira Souza
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Cone-Compactness of a Set and Applications to Set-Equilibrium Problems J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-11 Marius Durea, Elena-Andreea Florea
We study the possibility to get a sequential characterization of the compactness of a set with respect to a cone. Then, we consider some set-equilibrium problems (whose formulations are inspired by set-optimization problems) and in the study of the existence of a solution of these problems we employ the generalized compactness investigated before. Several technical tools are needed throughout the presentation
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Well-Posedness for Mean Field Games with Finite State and Action Space J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-10 Lu-ping Liu, Wen-sheng Jia
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Relaxed-Inertial Proximal Point Algorithms for Nonconvex Equilibrium Problems with Applications J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-06 Sorin-Mihai Grad, Felipe Lara, Raúl Tintaya Marcavillaca
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Exact Controllability of Abstract Fractional Evolution Systems J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-02 He Yang
This paper studies the exact controllability of semilinear \(q\in (1,2)\)-order fractional evolution systems with a weighted delay initial condition in abstract spaces. Firstly, with the aid of properties of the strongly continuous cosine family, the expression of mild solutions of the concerned problem is presented. Exact controllability results are achieved under essential conditions on f. An example
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Exact SDP Reformulations for Adjustable Robust Quadratic Optimization with Affine Decision Rules J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-02 Huan Zhang, Xiangkai Sun, Kok Lay Teo
In this paper, we deal with exact semidefinite programming (SDP) reformulations for a class of adjustable robust quadratic optimization problems with affine decision rules. By virtue of a special semidefinite representation of the non-negativity of separable non-convex quadratic functions on box uncertain sets, we establish an exact SDP reformulation for this adjustable robust quadratic optimization
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Classification of Time-Optimal Paths Under an External Force Based on Jacobi Stability in Finsler Space J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-02-01 Takahiro Yajima, Yuna Tazawa
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A Regularization-Patching Dual Quaternion Optimization Method for Solving the Hand-Eye Calibration Problem J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-30
Abstract The hand-eye calibration problem is an important application problem in robot research. Based on the 2-norm of dual quaternion vectors, we propose a new dual quaternion optimization method for the hand-eye calibration problem. The dual quaternion optimization problem is decomposed to two quaternion optimization subproblems. The first quaternion optimization subproblem governs the rotation
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Role of Subgradients in Variational Analysis of Polyhedral Functions J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-29 Nguyen T. V. Hang, Woosuk Jung, Ebrahim Sarabi
Understanding the role that subgradients play in various second-order variational analysis constructions can help us uncover new properties of important classes of functions in variational analysis. Focusing mainly on the behavior of the second subderivative and subgradient proto-derivative of polyhedral functions, i.e., functions with polyhedral convex epigraphs, we demonstrate that choosing the underlying
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Errata of the Unique Solvability of the Absolute Value Equation J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-27 Shi-Liang Wu, Peng Guo
A published counterexample motivates us to correct one of our theorems in the previously published work in Wu and Guo (J Optim Theory Appl 169:705–712, 2016).
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Shifted Inverse Power Method for Computing the Smallest M-Eigenvalue of a Fourth-Order Partially Symmetric Tensor J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-24 Jianxing Zhao, Pin Liu, Caili Sang
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Robust Matching for Teams J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-21 Daniel Owusu Adu, Bahman Gharesifard
We examine a hedonic model featuring uncertain production costs. The aim is to determine equilibrium prices and wages that facilitate the pairing of consumers with teams of producers, even when faced with the veil of uncertainty shrouding production costs. Using the framework of optimal transport theory, we identify the conditions sufficient for the existence of robust matching equilibrium. Our results
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Impulse Control of Conditional McKean–Vlasov Jump Diffusions J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-19
Abstract In this paper, we consider impulse control problems involving conditional McKean–Vlasov jump diffusions, with the common noise coming from the \(\sigma \) -algebra generated by the first components of a Brownian motion and an independent compensated Poisson random measure. We first study the well-posedness of the conditional McKean–Vlasov stochastic differential equations (SDEs) with jumps
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On Local Behavior of Newton-Type Methods Near Critical Solutions of Constrained Equations J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-17 A. F. Izmailov, M. V. Solodov
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Polyhedral Approximation of Spectrahedral Shadows via Homogenization J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-17 Daniel Dörfler, Andreas Löhne
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An Outer Space Approach to Tackle Generalized Affine Fractional Program Problems J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-16 Hongwei Jiao, Binbin Li, Youlin Shang
This paper aims to globally solve a generalized affine fractional program problem (GAFPP). Firstly, by introducing some outer space variables and performing equivalent transformations, we can derive the equivalence problem (EP) of the GAFPP. Secondly, by constructing a novel linear relaxation method, we can deduce the affine relaxation problem (ARP) of the EP. Next, by solving the ARP to compute the
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Inverse Vertex/Absolute Quickest 1-Center Location Problem on a Tree Under Weighted $$l_1$$ Norm J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-14 Xinqiang Qian, Xiucui Guan, Junhua Jia, Panos M. Pardalos
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Correction to: On the Unique Solvability of the Absolute Value Equation J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-13 Shubham Kumar
In this note, we give the two counterexamples for two unique solvability conditions that appeared in the published paper by Wu et al. (J Optim Theory Appl 169:705–712, 2016).
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Optimality Conditions for Nondifferentiable Minimax Programs and Vector Optimization Problems J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-12
Abstract First-order sufficient optimality conditions in terms of Lagrangian functions and Lagrange multipliers for nondifferentiable minimax programs and vector optimization problems in an Asplund space setting are obtained in this paper. Two illustrative examples are given. Our results implement the first-order necessary optimality conditions of Chuong and Kim (Ann Oper Res 251:73–87, 2017).
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Enhanced Computation of the Proximity Operator for Perspective Functions J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-10
Abstract In this paper, we provide an explicit expression for the proximity operator of a perspective of any proper lower semicontinuous convex function defined on a Hilbert space. Our computation enhances and generalizes known formulae for the case when the Fenchel conjugate of the convex function has an open domain or when it is radial. We show numerically that our approach is more efficient than
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Application of Hamilton–Jacobi–Bellman Equation/Pontryagin’s Principle for Constrained Optimal Control J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-09 Jerome Weston, Domagoj Tolić, Ivana Palunko
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Generalized Multilinear Games and Vertical Tensor Complementarity Problems J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-08 Qingyang Jia, Zheng-Hai Huang, Yong Wang
This paper generalizes the multilinear game where the payoff tensor of each player is fixed to the generalized multilinear game where the payoff tensor of each player is selected from a nonempty set of tensors. We prove the existence of \(\varepsilon \)-Nash equilibria for generalized multilinear games under the assumption that all involved sets of tensors are bounded, and the existence of Nash equilibria
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Global Error Bound for the Vertical Tensor Complementarity Problem J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-07
Abstract As a natural extension of the tensor complementarity problem, the vertical tensor complementarity problem \(\left( {\textrm{VTCP}}\right) \) has important research value. In this paper, we get some properties of the solution of the VTCP. Furthermore, we focus on investigating the global error bound for the VTCP with the type \({\textrm{VP}}\) tensor set. We define two positively homogeneous
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Observability Inequality from Measurable Sets for Degenerate Parabolic Equations and its Applications J. Optim. Theory Appl. (IF 1.9) Pub Date : 2024-01-04 Yuanhang Liu, Weijia Wu, Donghui Yang, Can Zhang
In this study, we employ the established Carleman estimates and propagation estimates of smallness from measurable sets for real analytic functions, along with the telescoping series method, to establish an observability inequality for the degenerate parabolic equation over measurable subsets in the time-space domain. As a direct application, we formulate a captivating Stackelberg–Nash game problem
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A New Approach About Equilibrium Problems via Busemann Functions J. Optim. Theory Appl. (IF 1.9) Pub Date : 2023-12-27
Abstract In this paper, we consider the resolvent via Busemann functions introduced by Bento, Cruz Neto, Melo (J Optim Theory Appl 195:1087–1105, 2022), and we present a proximal point method for equilibrium problems on Hadamard manifold. The resolvent in consideration is a natural extension of its counterpart in linear settings, proposed and analyzed by Combettes and Hirstoaga (J Nonlinear Convex
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An Inexact Primal-Dual Smoothing Framework for Large-Scale Non-Bilinear Saddle Point Problems J. Optim. Theory Appl. (IF 1.9) Pub Date : 2023-12-22 Le Thi Khanh Hien, Renbo Zhao, William B. Haskell
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Existence of Equilibrium Solution for Multi-Leader–Follower Games with Fuzzy Goals and Parameters J. Optim. Theory Appl. (IF 1.9) Pub Date : 2023-12-21 Zhenli Liu, Guoling Wang, Guanghui Yang
In this paper, we first propose the model of multi-leader–follower games with fuzzy goals involving fuzzy parameters and introduce its \(\alpha \)-FNS equilibrium. Next, we shift our attention to the existence of \(\alpha \)-FNS equilibrium and prove it by Kakutani’s fixed point theorem. Finally, we illustrate an example to show that the equilibrium existence result is valid.
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Strongly Convergent Inertial Proximal Point Algorithm Without On-line Rule J. Optim. Theory Appl. (IF 1.9) Pub Date : 2023-12-21 Lateef O. Jolaoso, Yekini Shehu, Jen-Chih Yao
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On Stochastic Roundoff Errors in Gradient Descent with Low-Precision Computation J. Optim. Theory Appl. (IF 1.9) Pub Date : 2023-12-20
Abstract When implementing the gradient descent method in low precision, the employment of stochastic rounding schemes helps to prevent stagnation of convergence caused by the vanishing gradient effect. Unbiased stochastic rounding yields zero bias by preserving small updates with probabilities proportional to their relative magnitudes. This study provides a theoretical explanation for the stagnation
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On Computing Medians of Marked Point Process Data Under Edit Distance J. Optim. Theory Appl. (IF 1.9) Pub Date : 2023-12-20 Noriyoshi Sukegawa, Shohei Suzuki, Yoshiko Ikebe, Yoshito Hirata
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Proximal Gradient Method with Extrapolation and Line Search for a Class of Non-convex and Non-smooth Problems J. Optim. Theory Appl. (IF 1.9) Pub Date : 2023-12-19
Abstract In this paper, we consider a class of possibly non-convex and non-smooth optimization problems arising in many contemporary applications such as machine learning, variable selection and image processing. To solve this class of problems, we propose a proximal gradient method with extrapolation and line search (PGels). This method is developed based on a special potential function and successfully
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Behavior of Newton-Type Methods Near Critical Solutions of Nonlinear Equations with Semismooth Derivatives J. Optim. Theory Appl. (IF 1.9) Pub Date : 2023-12-18 Andreas Fischer, Alexey F. Izmailov, Mario Jelitte
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Algorithms for Cardinality-Constrained Monotone DR-Submodular Maximization with Low Adaptivity and Query Complexity J. Optim. Theory Appl. (IF 1.9) Pub Date : 2023-12-18 Suning Gong, Qingqin Nong, Jiazhu Fang, Ding-Zhu Du