Zhongping Wan

• Wuhan University

This paper focuses on bilevel programs with a convex lower-level problem violating Slater’s constraint qualification. We relax the constrained domain of the lower-level problem. Then, an approximate solution of the original bilevel program can be obtained by solving this perturbed bilevel program. As the lower-level problem of the perturbed bilevel...

In this paper, we present a new solving approach for a class of multi-leader–follower games. For the problem studied, we firstly propose a neural network model. Then, based on Lyapunov and LaSalle theories, we prove that the trajectory of the neural network model can converge to the equilibrium point, which corresponds to the Nash equilibrium of th...

In this paper, we are interested by the linear bilevel multiobjective programming problem, where both the upper level and the lower level have multiple objectives. We approach this problem via an exact penalty method. Then, we propose an exact penalty function algorithm. Numerical results showing viability of the algorithm proposed are presented.

In this paper we consider a class of bilevel variational inequalities with hierarchical nesting structure. We first of all get the existence of a solution for this problem by using the Himmelberg fixed point theorem. Then the uniqueness of the solution for an upper-level variational inequality is given under some mild conditions. By using gap funct...

Multilevel programming problems model a decision-making process with a hierarchy structure. Traditional solution methods including vertex enumeration algorithms and penalty function methods are not only inefficient to obtain the solution of the multilevel programming problems, but also lead to a paradox that the follower’s decision power dominates...

This paper mainly studies the optimality conditions for a class of pessimistic trilevel optimization problem, of which middle-level is a pessimistic problem. We firstly translate this problem into an auxiliary pessimistic bilevel optimization problem, by applying KKT approach for the lower level problem. Then we obtain a necessary optimality condit...

The focus of this' paper is to investigate optimality conditions for a class of multiobjective optimization problems with cone constraints (in short, MOP). The image space analysis associated to MOP is introduced. We prove that a weakly efficient solution for MOP can be equivalently expressed in terms of the disjunction of two suitable subsets of t...

In this paper, by using Bregman's technique, we introduce and study the hybrid proximal-point methods for finding a common element of the set of solutions to a system of generalized equilibrium Problems and zeros of a finite family of maximal monotone operators in reflexive Banach spaces. Strong convergence results of the proposed hybrid proximal-p...

A novel inexact smoothing method is presented for solving the second-order cone complementarity problems (SOCCP). Our method reformulates the SOCCP as an equivalent nonlinear system of equations by introducing a regularized Chen-Harker-Kanzow-Smale smoothing function. At each iteration, Newton's method is adopted to solve the system of equations ap...

In this paper, we introduce and investigate two new generalized mixed equilibrium problems and explore the relationship between them and the properties of their solutions in Banach spaces. Based on the generalized f-projection, we construct hybrid algorithms to find common fixed points of a countable family of quasi-φ-nonexpansive mappings in Banac...

In this paper, we obtain the solution to bi-level linear fractional programming problem (BLFP) by means of an optimization algorithm based on the duality gap of the lower level problem. In our algorithm, the bi-level linear fractional programming problem is transformed into an equivalent single level programming problem by forcing the dual gap of t...

In this paper a filled function algorithm is applied to compute one of the nonisolated Pareto optimal points of an unconstrained multiobjective optimization problem. Firstly, the original problem is converted into an equivalent global optimization problem. Subsequently, a novel filled function algorithm is presented for solving the corresponding gl...

The penalty function method, presented many years ago, is an important nu-merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func-tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programm...

This paper presents a dual approach method of the bilevel linear programming which is based on the bilevel programming problem with the optimal value of the lower level problem feeding back to the upper level.

This paper proposes an algorithm for solution of the linear multilevel programming problem with global optimality by use of a novel current equivalent plane technique. An extreme point enumeration algorithm is presented that makes use of this technique and an example is given for a three level problem. Global optimality in finite number of iteratio...

In this paper, we focus on bilevel programming problem with a common decision variable in the upper level and lower level programming. After introducing fuzzy goals for objective functions, a fuzzy interactive decision making method is presented to derive a satisfactory solution for decision makers by consulting the ratios of satisfaction between t...

A new algorithm-approximate penalty function method is designed, which can be used to solve a bilevel optimization problem with linear constrained function. In this kind of bilevel optimization problem, the evaluation of the objective function is very difficult, so that only their approximate values can be obtained. This algorithm is obtained by co...