We consider a smooth pessimistic bilevel optimization problem, where the lower-level problem is convex and satisfies the Slater constraint qualification. These assumptions ensure that the Karush-Kuhn-Tucker (KKT) reformulation of our problem is well-defined. We then introduce and study the (i) Scholtes, (ii) Lin and Fukushima, (iii) Kadrani, Dussault and Benchakroun, (iv) Steffensen and Ulbrich, and … Read more
Optimization problems with cardinality constraints are very dicult mathematical programs which are typically solved by global techniques from discrete optimization. Here we introduce a mixed-integer formulation whose standard relaxation still has the same solutions (in the sense of global minima) as the underlying cardinality-constrained problem; the relation between the local minima is also discussed in … Read more
The elastic-mode formulation of the problem of minimizing a nonlinear function subject to equilibrium constraints has appealing local properties in that, for a finite value of the penalty parameter, local solutions satisfying first- and second-order necessary optimality conditions for the original problem are also first- and second-order points of the elastic-mode formulation. Here we study … Read more