IOR Preprint 2/2012
O. Stein:
How to solve a semi-infinite optimization problem
Abstract: After an introduction to main ideas of semi-infinite optimization, this article surveys recent developments in theory and numerical methods for standard and generalized semi-infinite optimization problems. Particular attention is paid to connections with mathematical programs with complementarity constraints, lower level Wolfe duality, semi-smooth approaches, as well as branch and bound techniques in adaptive convexification procedures. A section on recent genericity results includes a discussion of the symmetry effect in generalized semi-infinite optimization.
Keywords: Semi-infinite optimization, design centering, robust optimization, mathematical program with complementarity constraints, Wolfe duality, semi-smooth equation, adaptive convexification, genericity, symmetry.
AMS Subject Classification: 90C34, 90C30, 49M37, 65K10, 00-02.
IOR Preprint 1/2012
N. Harms, C. Kanzow, O. Stein:
On differentiability properties of player convex generalized Nash equilibrium problems
Abstract: This article studies differentiability properties for a reformulation of a player convex generalized Nash equilibrium problem as a constrained and possibly nonsmooth minimization problem. By using several results from parametric optimization we show that, apart from exceptional cases, all locally minimal points of the reformulation are differentiability points of the objective function. This justifies a numerical approach which basically ignores the possible nondifferentiabilities.
Keywords: Generalized Nash equilibrium problem, player convexity, Nikaido-Isoda function, Gateaux differentiability, Frechet differentiability, parametric optimization.
AMS Subject Classification: 91A10, 90C31.