The Noncooperative Fixed Charge Transportation Problem

We introduce the noncooperative fixed charge transportation problem (NFCTP), which is a game-theoretic extension of the fixed charge transportation problem. In the NFCTP, competing players solve coupled fixed charge transportation problems simultaneously. Three versions of the NFCTP are discussed and compared, which differ in their treatment of shared social costs. This may be used from … Read more

Granularity in nonlinear mixed-integer optimization

We study a deterministic technique to check the existence of feasible points for mixed-integer nonlinear optimization problems which satisfy a structural requirement that we call granularity. We show that solving certain purely continuous optimization problems and rounding their optimal points leads to feasible points of the original mixed-integer problem, as long as the latter is … Read more

A feasible rounding approach for mixed-integer optimization problems

We introduce granularity as a sufficient condition for the consistency of a mixed-integer optimization problem, and show how to exploit it for the computation of feasible points: For optimization problems which are granular, solving certain linear problems and rounding their optimal points always leads to feasible points of the original mixed-integer problem. Thus, the resulting … Read more

A feasible rounding approach for granular optimization problems

We introduce a new technique to generate good feasible points of mixed-integer nonlinear optimization problems. It makes use of the so-called inner parallel set of the relaxed feasible set, which was employed in O. Stein, Error bounds for mixed integer linear optimization problems, Mathematical Programming, Vol. 156 (2016), 101-123, as well as O. Stein, Error … Read more

Solving linear generalized Nash equilibrium problems numerically

This paper considers the numerical solution of linear generalized Nash equilibrium problems. Since many methods for nonlinear problems require the nonsingularity of some second order derivative, standard convergence conditions are not satisfied in our linear case. We provide new convergence criteria for a potential reduction algorithm that allow its application to linear generalized Nash equilibrium … Read more

The cone condition and nonsmoothness in linear generalized Nash games

We consider linear generalized Nash games and introduce the so-called cone condition which characterizes the smoothness of the Nikaido-Isoda function under weak assumptions. The latter mapping arises from a reformulation of the generalized Nash equilibrium problem as a possibly nonsmooth optimization problem. Other regularity conditions like LICQ or SMFC(Q) are only sufficient for smoothness, but … Read more

On smoothness properties of optimal value functions at the boundary of their domain under complete convexity

This article studies continuity and directional differentiability properties of optimal value functions, in particular at boundary points of their domain. We extend and complement standard continuity results from W.W. Hogan, Point-to-set maps in mathematical programming, SIAM Review, Vol. 15 (1973), 591-603, for abstract feasible set mappings under complete convexity as well as standard differentiability results … Read more