Web3. Properties of pessimistic bilevel optimization According to the definitions in Section 2, we cate-gorize the various properties of pessimistic bilevel optimization, and then list some of the well-known properties. 3.1. Existence of solutions As is well-known, the study of existence of solu-tions for pessimistic bilevel optimization is a diffi- WebExample 1. Consider the following instance of the pessimistic bi-level problem. minimize x x subject to x y 8y2argmin z z2: z2[ 1;1] x2R The lower-level problem is optimized by z2f 1;1g, independent of the upper-level decision. The pessimistic bi-level problem therefore requires xto exceed 1, resulting in an optimal objective value of 1. In ...

‪Lorenzo Lampariello‬ - ‪Google Scholar‬

WebWe study a variant of the pessimistic bilevel optimization problem, which comprises constraints that must be satisfied for any optimal solution of a subordinate (lower-level) optimization problem. ... We also present a computational study that illustrates the numerical behavior of our algorithm on standard benchmark instances. Date issued 2013 ... Web27.03.19: On pessimistic bilevel optimization, Computational Management Science / Mathematical Methods in Industry and Economics 2024, Chemnitz, Germany, March 27 - 29, 2024. 05.07.18: Global optimization of generalized semi-infinite programs using disjunctive programming, 23nd International Symposium on Mathematical Programming, Bordeaux ... budanko travel

Gradient-based Algorithms for Pessimistic Bilevel Optimization

WebFeb 3, 2024 · In particular, the α-pessimistic bilevel problem includes the standard pessimistic bilevel problem as well as the min-max problem by either setting α = 1 or α = 0, respectively. As an extension of the proposed model, the authors further embed an α -pessimistic follower into the context of strong-weak bilevel problems; see Section 3.5 . WebJun 29, 2024 · We first show that disjoint bilinear optimization problems can be cast as two-stage robust linear optimization problems with fixed-recourse and right-hand-side uncertainty, which enables us to apply robust optimization techniques to solve the resulting problems. To this end, a solution scheme based on a blending of three popular robust ... Weblevel problem, NORBiP with = 0 is therefore equivalent to the pessimistic bilevelproblemasformulatedin[2]: f(x;y) ˚(x) 8y2Z(x;0): For <0,Z(x; ) istheemptyset,inwhichcaseProblem(3)isequivalentto the original optimistic bilevel problem while the set Z(x;1) corresponds to thecompletelower-levelfeasibleset,assumingthelower … budaorskonyvtar