Gauss–Newton-type methods for bilevel optimization

Abstract This article studies Gauss–Newton-type methods for over-determined systems to find solutions bilevel programming problems. To proceed, we use the lower-level value function reformulation of programs and consider necessary optimality conditions under appropriate assumptions. First, strict complementarity upper- feasibility constraints, prove convergence a method in computing points satisfying these additional tractable qualification conditions. Potential approaches address shortcomings are then proposed, leading alternatives such as pseudo or smoothing optimization. Our numerical experiments conducted on 124 examples from recently released Bilevel Optimization LIBrary (BOLIB) compare performance our different scenarios show that it is approach solve optimization problems with continuous variables.