We classify functions $$f:(a,b)\rightarrow \mathbb {R}$$ which satisfy the inequality $$\begin{aligned} {\text {tr}}f(A)+f(C)\ge {tr}}f(B)+f(D) \end{aligned}$$ when $$A\le B\le C$$ are self-adjoint matrices, $$D= A+C-B$$ , so-called trace minmax functions. (Here B$$ if $$B-A$$ is positive semidefinite, and f evaluated via functional calculus.) A function only its derivative analytically continu...

In this paper the minmax (regret) versions of some basic polynomially solvable deterministic network problems are discussed. It is shown that if the number of scenarios is unbounded, then the problems under consideration are not approximable within logK for any ǫ > 0 unless NP ⊆ DTIME(n log ), where K is the number of scenarios.

We establish an existence result for a class of quasilinear elliptic boundary value problems with jumping nonlinearities using variational arguments. First we calculate certain homotopy groups of sublevel sets of the asymptotic part of the variational functional. Then we use these groups to show that the full functional admits a linking geometry and hence a minmax critical point.

The perfect monitoring assumption is replaced by a signalling structure that models, for each player, the information about the opponent’s previous action. The value of a stochastic game may not exist any more. For the class of absorbing games, we are able to show the existence of the maxmin and the minmax. The value does not exist if they are different.

In this paper we survey variational characterizations of eigenvalues of nonlinear eigenproblems, i.e. generalizations of Rayleigh’s principle, the minmax characterization of Poincaré, and the maxmin characterization of Courant, Fischer and Weyl to eigenvalue problems containing the eigenparameter nonlinearly. In this note we consider the nonlinear eigenvalue problem