In this paper we consider bilevel programming problems in which the lower level problem is not assumed to have unique optimal solutions for all values of the parameter. Using common approaches to treat such problems, a generally discontinuous function is to be minimized. This leads to the deenition of a new class of functions, so-called generalized PC 1-functions which are composed by a nite nu...

———————————————————————————————Abstract In sciences and industries such as signal optimization, traffic assignment, economic market and etc, many problems have been modeled by bilevel programming (BLP) problems, where in each level one must optimize some objective functions. There are so many algorithms in order to find the global optimum of the linear version of BLP problems. This paper addres...

This document discusses the aspects of network design.First a brief introduction of network design will be given.Then various types of assignment techniques will be discussed including the mathematical formulation and numerical illustration of the important ones.Then the concept of bilevel programming and few examples will be presented.Finally one such example, namely the network capacity expan...

In a bilevel decision problem, the leader at the upper level attempts to optimize his/her objective, the follower at the lower level tries to find an optimized strategy according to each of possible decisions made by the leader. A bilevel decision problem may involve fuzzy demands which appear either in the objective functions or constraints of the leader or the follower or both. Furthermore, t...

The paper is devoted to applications of advanced tools of modern variational analysis and generalized differentiation to problems of optimistic bilevel programming. In this way, new necessary optimality conditions are derived for two major classes of bilevel programs: those with partially convex and with fully convex lower-level problems. We provide detailed discussions of the results obtained ...

In this paper we discuss special bilevel optimal control problems where the upper level problem is an optimal control problem of ODEs with control and terminal constraints and the lower level problem is a finite-dimensional parametric optimization problem where the parameter is the final state of the state variable of the upper level. We tackle this problem using tools of nonsmooth analysis, op...

In this note, we analyze a bilevel interdiction problem, where the follower’s program is a parametrized continuous knapsack. Based on the structure of the problem and an inverse optimization strategy, we propose for its solution an algorithm with worst-case complexity O(n). Keywords— Bilevel programming, Continuous knapsack problem, Polynomial time. 1 Model Recently, a number of papers have bee...