We study the split common fixed point problem for Bregman relatively nonexpansive operators and the split feasibility problem with multiple output sets in real reflexive Banach spaces. Using Bregman distances, we propose several new cyclic projection algorithms for solving these problems.

We introduce a variational approach to study a maximization problem of preferences that cannot be represented by a utility function. In such conditions, we reformulate the problem as a suitable variational problem and we give regularity properties of the solutions map. The theoretical results are applied in studying an equilibrium problem under uncertainty.

In this paper, we give some properties concerned with weak minimal solutions of nonconvex set optimization problems. We also give some properties of the nonconvex separation functional and apply them to characterize weak minimal solutions of nonconvex set optimization problems. Moreover, we derive some new existence results for weak minimal solutions of nonconvex set optimization problems whose image

The class of quaternion matrix optimization (QMO) problems, with quaternion matrices as decision variables, has been widely used in color image processing and other engineering areas in recent years. However, optimization theory for QMO is far from adequate. The main objective of this paper is to provide necessary theoretical foundations on optimality analysis, in order to enrich the contents of optimization

The present work was primarily motivated by our findings in the literature of some flaws within the proof of the second-order Legendre necessary optimality condition for fractional calculus of variations problems. Therefore, we were eager to elaborate a correct proof and it turns out that this goal is highly nontrivial, especially when considering final constraints. This paper is the result of our

A composite control law for stabilizing a small-scale helicopter during hover flight mode is proposed in this paper. The proposed method is developed by combining the sliding mode control (SMC) and a nonlinear control law. Parameters of the proposed controller are optimized using particle swarm optimization technique. The SMC ensures robustness under disturbances and parameter uncertainties, while

This paper proposes an optimal control design framework for hybrid nonlinear time-dependent dynamical systems involving an interacting mixture of continuous-time and discrete-time dynamics. Aiming to extend hybrid linear optimal control synthesis to nonlinear non-quadratic formulation, a hybrid version of the Hamilton–Jacobi–Bellman (HJB) equation with time-dependency is first presented. A hybrid computational

A projected extrapolated gradient method is designed for solving monotone variational inequality in Hilbert space. Requiring local Lipschitz continuity of the operator, our proposed method improves the value of the extrapolated parameter and admits larger step sizes, which are predicted based a local information of the involved operator and corrected by bounding the distance between each pair of successive

An existence result for a generalized inequality over a possible unbounded domain in a finite-dimensional space is established. The proof technique allows to avoid any monotonicity assumption. We adapt a weak coercivity condition introduced in Castellani and Giuli (J Glob Optim 75:163–176, 2019) for a generalized game which extends an older one proposed by Konnov and Dyabilkin (J Glob Optim 49:575–577

Direct optimization of many-revolution spacecraft trajectories is performed using an unconstrained formulation with many short-arc, embedded Lambert problems. Each Lambert problem shares its terminal positions with neighboring segments to implicitly enforce position continuity. Use of embedded boundary value problems (EBVPs) is not new to spacecraft trajectory optimization, including extensive use

Every maximally monotone operator can be associated with a family of convex functions, called the Fitzpatrick family or family of representative functions. Surprisingly, in 2017, Burachik and Martínez-Legaz showed that the well-known Bregman distance is a particular case of a general family of distances, each one induced by a specific maximally monotone operator and a specific choice of one of its

We are concerned with the tensor equations whose coefficient tensors are M-tensors. We first propose a Newton method for solving the equation with a positive constant term and establish its global and quadratic convergence. Then we extend the method to solve the equation with a nonnegative constant term and establish its convergence. At last, we do numerical experiments to test the proposed methods

This paper proposes a convex-optimization-based relatively optimal controller (ROC) for the attitude regulation of 3 degree of freedom (DOF) tandem helicopter utilizing feedback linearization (FBL). The constant velocity in the pseudo-active axis achieved by regulating two active axes results in the motion of the helicopter in a circular path at a specified altitude. The FBL helps in transforming the

Sample average approximation (SAA) approach for two-stage stochastic variational inequalities (SVIs) with continuous probability distributions, where the second-stage problems have multiple solutions, may not promise convergence assertions as the sample size tends to infinity. In this paper, a regularized SAA approach is proposed to numerically solve a class of two-stage SVIs with continuous probability

Pollution management models of Shallow Lake type identify a well-known class of infinite horizon optimal control problems, characterized by the absence of concavity in the state equation and of compactness in the control space. The seminal paper by Mäler et al. (2003) generated a consistent stream of literature over the years, even though existence of solutions to the optimization problem had for long

We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed spaces. Based on such a representation, we study a fully piecewise linear vector optimization problem with the objective and constraint functions being piecewise linear. To solve this problem, we divide it into some linear subproblems and structure a dimensional

Nowadays, large part of the technical knowledge associated with collapses of slabs is based on past failures of bridges, floors, flat roofs and balconies. Collapse mechanisms tend to often differ from each other due to unique features which make it difficult to derive a generalised technique that can predict the right mechanism. This paper proposes a novel algorithm for tackling the problem of detection

We consider the game of a holonomic evader passing between two holonomic pursuers. The optimal trajectories of this game are known. We give a detailed explanation of the game of kind’s solution and present a computationally efficient way to obtain trajectories numerically by integrating the retrograde path equations. Additionally, we propose a method for calculating the partial derivatives of the Value

In this paper, we investigate the manifolds of three Near-Rectilinear Halo Orbits (NRHOs) and optimal low-thrust transfer trajectories using a high-fidelity dynamical model. Time- and fuel-optimal low-thrust transfers to (and from) these NRHOs are generated leveraging their ‘invariant’ manifolds, which serve as long terminal coast arcs. Analyses are performed to identify suitable manifold entry/exit

We present the second-order point-based (necessary and sufficient) optimality conditions for nonlinear programming with continuously differentiable data, via the regular and limiting (Mordukhovich) second-order subdifferentials. The sharper results are obtained for \(C^{1,1}\) data. Also, we derive a second-order characterization for (strictly and strongly) pseudoconvex, continuously differentiable

In this paper, the first-order forward–backward–half forward dynamical systems associated with the inclusion problem consisting of three monotone operators are analyzed. The framework modifies the forward–backward–forward dynamical system by adding a cocoercive operator to the inclusion. The existence, uniqueness, and weak asymptotic convergence of the generated trajectories are discussed. A variable

We show that Malitsky’s recent Golden Ratio Algorithm for solving convex mixed variational inequalities can be employed in a certain nonconvex framework as well, making it probably the first iterative method in the literature for solving generalized convex mixed variational inequalities, and illustrate this result by numerical experiments.

In this paper, we propose new approximation algorithms for a NP-hard problem, i.e., weighted maximin dispersion problem. By using a uniformly distributed random sample method, we first propose a new random approximation algorithm for box constrained or ball constrained weighted maximin dispersion problems and analyze its approximation bound respectively. Moreover, we propose two improved approximation

In this paper, we study a first-order solution method for a particular class of set optimization problems where the solution concept is given by the set approach. We consider the case in which the set-valued objective mapping is identified by a finite number of continuously differentiable selections. The corresponding set optimization problem is then equivalent to find optimistic solutions to vector

In this paper, we give an overview on optimality conditions and exact penalization for the mathematical program with switching constraints (MPSC). MPSC is a new class of optimization problems with important applications. It is well known that if MPSC is treated as a standard nonlinear program, some of the usual constraint qualifications may fail. To deal with this issue, one could reformulate it as

In the study of stochastic variational inequalities, the extragradient algorithms attract much attention. However, such schemes require two evaluations of the expected mapping at each iteration in general. In this paper, we present several variance-based single-call proximal extragradient algorithms for solving a class of stochastic mixed variational inequalities by aiming at alleviating the cost of

We study a first-order primal-dual subgradient method to optimize risk-constrained risk-penalized optimization problems, where risk is modeled via the popular conditional value at risk (CVaR) measure. The algorithm processes independent and identically distributed samples from the underlying uncertainty in an online fashion and produces an \(\eta /\sqrt{K}\)-approximately feasible and \(\eta /\sqr

We consider exact and averaged control problem for a system of quasilinear ODEs and SDEs with a nonnegative definite symmetric matrix of the system. The strategy of the proof is the standard linearization of the system by fixing the function appearing in the nonlinear part of the system and then applying the Leray–Schauder fixed point theorem. We shall also need the continuous induction arguments to

In this paper, we propose and analyze a variant of the proximal point method for obtaining weakly efficient solutions of convex vector optimization problems in real Hilbert spaces, with respect to a partial order induced by a closed, convex and pointed cone with nonempty interior. The proposed method is a hybrid scheme that combines proximal point type iterations and projections onto some special halfspaces

Minibatch decomposition methods for empirical risk minimization are commonly analyzed in a stochastic approximation setting, also known as sampling with replacement. On the other hand, modern implementations of such techniques are incremental: they rely on sampling without replacement, for which available analysis is much scarcer. We provide convergence guaranties for the latter variant by analyzing

We consider the classical inverse mapping theorem of Nash and Moser from the angle of some recent development by Ekeland and the authors. Geometrisation of tame estimates coupled with certain ideas coming from variational analysis when applied to a directionally differentiable mapping produces very general surjectivity result and, if injectivity can be ensured, inverse mapping theorem with the expected

This paper proposes and analyzes a globalized version of the Newton method for finding a singularity of the nonsmooth vector fields. Basically, the new method combines a version of nonsmooth Newton method with a nonmonotone line search strategy. The global convergence analysis of the proposed method as well as results on its rate are established under mild assumptions. Finally, numerical experiments

We propose BIBPA, a block inertial Bregman proximal algorithm for minimizing the sum of a block relatively smooth function (that is, relatively smooth concerning each block) and block separable nonsmooth nonconvex functions. We show that the cluster points of the sequence generated by BIBPA are critical points of the objective under standard assumptions, and this sequence converges globally when a

In this paper, we propose in a Hilbertian setting a second-order time-continuous dynamic system with fast convergence guarantees to solve structured convex minimization problems with an affine constraint. The system is associated with the augmented Lagrangian formulation of the minimization problem. The corresponding dynamics brings into play three general time-varying parameters, each with specific

Recent advancements in the sensor industry, smart metering systems and communication technology have led to interesting electricity consumption optimization opportunities that contribute to both peak reduction and bill savings and better integration of flexible appliances (including e-mobility). In combination with advanced tariffs, there has been a promising demand side management strategy devised

The purpose of this paper is to provide a new scheduling model of a large constellation of imaging satellites that does not use a heuristic solving method. The objective is to create a mixed-integer linear model that would be competitive in speed and in its closeness to reality against a current model using simulated annealing, while trying to improve both models. Each satellite has the choice between

As an extension of the complementarity problem (CP), the weighted complementarity problem (wCP) is a large class of equilibrium problems with wide applications in science, economics, and engineering. If the weight vector is zero, the wCP reduces to a CP. In this paper, we present a full-Newton step infeasible interior-point method (IIPM) for the special weighted linear complementarity problem over

We introduce a reformulation technique that converts a many-set feasibility problem into an equivalent two-set problem. This technique involves reformulating the original feasibility problem by replacing a pair of its constraint sets with their intersection, before applying Pierra’s classical product space reformulation. The step of combining the two constraint sets reduces the dimension of the product

This paper considers sufficient descent Riemannian conjugate gradient methods with line search algorithms. We propose two kinds of sufficient descent nonlinear conjugate gradient method and prove that these methods satisfy the sufficient descent condition on Riemannian manifolds. One is a hybrid method combining a Fletcher–Reeves-type method with a Polak–Ribière–Polyak-type method, and the other is

In this paper, we propose a projected subgradient method for solving constrained nondifferentiable quasiconvex multiobjective optimization problems. The algorithm is based on the Plastria subdifferential to overcome potential shortcomings known from algorithms based on the classical gradient. Under suitable, yet rather general assumptions, we establish the convergence of the full sequence generated

We consider shape optimization problems involving functionals depending on perimeter, torsional rigidity and Lebesgue measure. The scaling free cost functionals are of the form \(P(\Omega )T^q(\Omega )|\Omega |^{-2q-1/2}\), and the class of admissible domains consists of two-dimensional open sets \(\Omega \) satisfying the topological constraints of having a prescribed number k of bounded connected

The detection of optimal trajectories with multiple coast arcs represents a significant and challenging problem of practical relevance in space mission analysis. Two such types of optimal paths are analyzed in this study: (a) minimum-time low-thrust trajectories with eclipse intervals and (b) minimum-fuel finite-thrust paths. Modified equinoctial elements are used to describe the orbit dynamics. Problem

In this work, we develop a level-set subdifferential error bound condition with an eye toward convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. It is proved that the aforementioned condition guarantees linear convergence of VBPG and is weaker than Kurdyka–Łojasiewicz property, weak metric subregularity

We introduce a new framework for unifying and systematizing the performance analysis of first-order black-box optimization algorithms for unconstrained convex minimization. The low-cost iteration complexity enjoyed by first-order algorithms renders them particularly relevant for applications in machine learning and large-scale data analysis. Relying on sum-of-squares (SOS) optimization, we introduce

Necessary optimality conditions for a bilevel optimization problem are given in the paper by Kohli (J Optim Theory Appl 152: 632–651, 2012). Recently, the same author corrected his results in the note (J Optim Theory Appl 181:706–707, 2019). In this work, we have pointed out that some of the new modifications are wrong. We correct the flaws and present an alternative proof for the main result.

We study the optimum correction of infeasible systems of linear inequalities through making minimal changes in the coefficient matrix and the right-hand side vector by using the Frobenius norm. It leads to a special structured unconstrained nonlinear and nonconvex problem, which can be reformulated as a one-dimensional parametric minimization problem such that each objective function corresponds to

In this paper, we deal with the weakly homogeneous generalized variational inequality, which provides a unified setting for several special variational inequalities and complementarity problems studied in recent years. By exploiting weakly homogeneous structures of involved map pairs and using degree theory, we establish a result which demonstrates the connection between weakly homogeneous generalized

In continuation of the work in Leventides and Petroulakis (Adv Appl Clifford Algebras 27:1503–1515, 2016), Leventides et al. (J Optim Theory Appl 169(1):1–16, 2016), which defines extremal varieties in \(\mathbb {P}\left( {{ \bigwedge ^2}{\mathbb {R}^n}} \right) \), we define a more general concept of extremal varieties of the real Grassmannian \({G_p}\left( {{\mathbb {R}^n}} \right) \) in \(\mathbb

A correction to this paper has been published: https://doi.org/10.1007/s10957-020-01779-7.

This work presents an online decentralized allocation algorithm of a safety-critical application on parallel computing architectures, where individual Computational Units can be affected by faults. The described method includes representing the architecture by an abstract graph where each node represents a Computational Unit. Applications are also represented by the graph of Computational Units they

In this paper, we first employ the subdifferential closedness condition and Guignard’s constraint qualification to present “dual cone characterizations” of the constraint set \( \varOmega \) with infinite nonconvex inequality constraints, where the constraint functions are Fréchet differentiable that are not necessarily convex. We next provide sufficient conditions for which the “strong conical hull

It is generally assumed that any set of players can form a feasible coalition for classical cooperative games. But, in fact, some players may withdraw from the current game and form a union, if this makes them better paid than proposed. Based on the principle of coalition split, this paper presents an endogenous procedure of coalition formation by levels and bargaining for payoffs simultaneously, where

A reformulation of cardinality-constrained optimization problems into continuous nonlinear optimization problems with an orthogonality-type constraint has gained some popularity during the last few years. Due to the special structure of the constraints, the reformulation violates many standard assumptions and therefore is often solved using specialized algorithms. In contrast to this, we investigate

Optimization of low-thrust trajectories is necessary in the design of space missions using electric propulsion systems. We consider the problem of limited power trajectory optimization, which is a well-known case of the low-thrust optimization problem. In the article, we present an indirect approach to trajectory optimization based on the use of the maximum principle and the continuation method. We

This work provides analysis of a variant of the Risk-Sharing Principal-Agent problem in a single period setting with additional constant lower and upper bounds on the wage paid to the Agent. The effect of the extra constraints on optimal contract existence is studied and leads to conditions on the underlying utility functions under which an optimum may be attained. Solution characterization is then

A simple multi-physical system for the potential flow of a fluid through a shroud, in which a mechanical component, like a turbine vane, is placed, is modeled mathematically. We then consider a multi-criteria shape optimization problem, where the shape of the component is allowed to vary under a certain set of second-order Hölder continuous differentiable transformations of a baseline shape with boundary

The features that characterize the onset of Huntington disease (HD) are poorly understood yet have significant implications for research and clinical practice. Motivated by the need to address this issue, and the fact that there may be inaccuracies in clinical HD data, we apply robust optimization and duality techniques to study support vector machine (SVM) classifiers in the face of uncertainty in

We consider an optimal control problem for non-isothermal steady flows of low-concentrated aqueous polymer solutions in a bounded 3D domain. In this problem, the state functions are the flow velocity and the temperature, while the control function is the heat flux through a given part of the boundary of the flow domain. We obtain sufficient conditions for the existence of weak solutions that minimize

The relationships between Greenberg–Pierskalla’s subdifferential and some variants of it and semi-quasidifferentials of quasiconvex functions are studied in this paper. Also, some characterizations of quasiconvex functions in terms of semi-quasidifferentials and the connection between quasimonotonicity of semi-quasidifferentials and quasiconvexity are investigated.

A popular approach to recover low rank matrices is the nuclear norm regularized minimization (NRM) for which the selection of the regularization parameter is inevitable. In this paper, we build up a novel rule to choose the regularization parameter for NRM, with the help of the duality theory. Our result provides a safe set for the regularization parameter when the rank of the solution has an upper