An interior-point trust-region algorithm to solve a nonlinear bilevel programming problem

<abstract><p>In this paper, a nonlinear bilevel programming (NBLP) problem is transformed into an equivalent smooth single objective nonlinear programming (SONP) problem utilized slack variable with a Karush-Kuhn-Tucker (KKT) condition. To solve the equivalent smooth SONP problem effectively, an interior-point Newton's method with Das scaling matrix is used. This method is locally method and to guarantee convergence from any starting point, a trust-region strategy is used. The proposed algorithm is proved to be stable and capable of generating approximal optimal solution to the nonlinear bilevel programming problem.</p> <p>A global convergence theory of the proposed algorithm is introduced and applications to mathematical programs with equilibrium constraints are given to clarify the effectiveness of the proposed approach.</p></abstract>

Optimality Conditions Using Convexifactors for a Multiobjective Fractional Bilevel Programming Problem

In this paper, a multiobjective fractional bilevel programming problem is considered and optimality conditions using the concept of convexifactors are established for it. For this purpose, a suitable constraint qualification in terms of convexifactors is introduced for the problem. Further in the paper, notions of asymptotic pseudoconvexity, asymptotic quasiconvexity in terms of convexifactors are given and using them sufficient optimality conditions are derived.

Optimality conditions for nonsmooth multiobjective bilevel optimization using tangential subdifferentials

In combining the value function approach and tangential subdifferentials, we establish necessary optimality conditions of a nonsmooth multiobjective bilevel programming problem under a suitable constraint qualification. The upper level objectives and constraint functions are neither assumed to be necessarily locally Lipschitz nor convex.

A Novel Technique for Solving Integer Linear Bilevel Programming Problems

A novel technique that addresses the solution of the general integer linear bilevel programming problem to global optimality is presented i.e. the general case of bilevel linear programming problems where each decision maker has objective functions conflicting with each other. We introduce linear programming problem of which resolution can permit to generate the whole feasible set of the upper level decisions. The approach is based on the relaxation of the feasible region by convex underestimation. Finally, we illustrate our approach with a numerical example.

The Backpropagation Artificial Neural Network Based on Elite Particle Swam Optimization Algorithm for Stochastic Linear Bilevel Programming Problem

For a class of stochastic linear bilevel programming problem, we firstly transform it into a deterministic linear bilevel covariance programming problem. Then, the deterministic bilevel covariance programming problem is solved by backpropagation artificial neural network based on elite particle swam optimization algorithm (BPANN-PSO). Finally, we perform the simulation experiments and the results show that the computational efficiency of the proposed algorithm has a potential upside compared with the classical algorithm.