arXiv subjects

Jian-Wen Peng

Publications and source records attributed to Jian-Wen Peng.

5 recordsLinked to original sources

arXiv2026

A two-step inertial method with a new step-size rule for variational inequalities in hilbert spaces

In this paper, a two-step inertial Tseng extragradient method involving self-adaptive and Armijo-like step sizes is introduced for solving variational inequalities with a quasimonotone cost function in the setting of a real Hilbert space. Weak convergence of the sequence generated by the proposed algorithm is proved without assuming the Lipschitz condition. An interesting feature of the proposed algorithm is its ability to select the better step size between the self-adaptive and Armijo-like options at each iteration step. Moreover, removing the requirement for the Lipschitz condition on the cost function broadens the applicability of the proposed method. Finally, the algorithm accelerates and complements several existing iterative algorithms for solving variational inequalities in Hilbert spaces.

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arXiv2025

Radial Epiderivative Based Fritz John and KKT Conditions in Nonsmooth Nonconvex Optimization

In this study, we examine Fritz John (FJ) and Karush-Kuhn-Tucker (KKT) type optimality conditions for a class of nonsmooth and nonconvex optimization problems with inequality constraints, where the objective and constraint functions all are assumed to be radially epidifferentiable. The concept of the radial epiderivative constitutes a distinct generalization of classical derivative notions, as it replaces the conventional limit operation with an infimum-based construction. This formulation permits the analysis of directional behavior without invoking standard neighborhood-based assumptions and constructions commonly required in generalized differentiation. This leads to one of the key advantages of the radial epiderivative which lies in its applicability even to discrete domains, where classical and generalized derivatives are often inapplicable or undefined. The other advantage of this concept is that it provides a possibility to inverstigate KKT conditions for global minimums. Consequently, this approach necessitates a reformulation of fundamental analytical tools such as gradient vectors, feasible direction sets, constraint qualifications and other concepts which are central to the derivation of optimality conditions in smooth optimization theory. The primary contribution of this paper is the development of a comprehensive theoretical framework for KKT conditions tailored to the radially epidifferentiable setting. We introduce novel definitions of the radial gradient vector, of the set of feasible directions, and examine how classical constraint qualifications may be interpreted and extended within this new framework.

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arXiv2023

Two nonmonotone multiobjective memory gradient algorithms

In this paper, two types of nonmonotone memory gradient algorithm for solving unconstrained multiobjective optimization problems are introduced. Under some suitable conditions, we show the convergence of the full sequence generated by the proposed algorithms to a weak Pareto optimal point

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arXiv2023

The Quasi-Newton Method for the Composite Multiobjective Optimization Problems

In this paper, we introduce several new quasi-Newton methods for the composite multiobjective optimization problems (in short, CMOP) with Armijo line search. These multiobjective versions of quasi-Newton methods include BFGS quasi-Newnon method, self-scaling BFGS quasi-Newnon method, and Huang BFGS quasi-Newnon method. Under some suitable conditions, we show that each accumulation point of the sequence generated by these algorithms, if exists, is both a Pareto stationary point and a Pareto optimal point of (CMOP).

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arXiv2022

Proximal Quasi-Newton Methods for Multiobjective Optimization Problems

We introduce some new proximal quasi-Newton methods for unconstrained multiobjective optimization problems (in short, UMOP), where each objective function is the sum of a twice continuously differentiable strongly convex function and a proper lower semicontinuous convex but not necessarily differentiable function. We propose proximal BFGS method, proximal self-scaling BFGS method, and proximal Huang BFGS method for (UMOP) with both line searches and without line searches cases. Under mild assumputions, we show that each accumulation point of the sequence generated by these algorithms, if exists, is a Pareto stationary point of the (UMOP). Moreover, we present their applications in both constrained multiobjective optimization problems and robust multiobjective optimization problems. In particular, for robust multiobjective optimization problems, we show that the subproblems of proximal quasi-Newton algorithms can be regarded as quadratic minimization problems with quadratic inequality constraints. Numerical experiments are also carried out to verify the effectiveness of the proposed proximal quasi-Newton methods.

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