Bhuvnesh Khatana

Second-Order Optimality Conditions for Bilevel Optimization Problems Using Parabolic Directional Derivatives

Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Convex Optimization

This paper studies the second-order properties of a class of inequality-constrained bilevel programming problems. First-order optimality conditions for the existence of solutions to bilevel optimization problems are derived using the first-order directional derivative of the optimal solution function of the lower-level problem in the seminal paper by Dempe (1992). In this work, we prove that … Read more

Descent Scheme for a Class of Bilevel Programming Problems

Categories Approximation Algorithms, Combinatorial Optimization, Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , ,

In this paper, a class of bilevel programming problems is studied, in which the lower level is a quadratic programming problem, and the upper level problem consists of a nonlinear objective function with coupling constraints. An iterative process is developed to generate a sequence of points, which converges to the solution of this problem. In … Read more