Optimization problems, variational inequalities, minimax problems can be formulated as equilibrium problems. The iterative algorithms of fixed points are often applied to finding the solution of equilibrium problems. In this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of fixed points of asymptotically nonexpansive mappings and the set of solution...

Combining the techniques of the working set identification and generalized gradient projection, we present a new generalized gradient projection algorithm for minimax optimization problems with inequality constraints. In this paper, we propose a new optimal identification function, from which we provide a new working set. At each iteration, the improved search direction is generated by only one...

We present simple one-shot distribution experiments comparing the relative importance of efficiency, maximin preferences and inequality aversion, as well as the relative performance of the fairness theories by Bolton and Ockenfels (2000) and Fehr and Schmidt (1999). While the Fehr and Schmidt model performs better in a direct comparison, this appears to be due to being in line with maximin pref...

In 1937, Von Neumann [1] established the famous coincidence theorem. Since then, the coincidence theorem was generalized in many directions. Browder [2] first proved some basic coincidence theorems for a pair of set-valued mappings in compact setting of topological vector spaces and gave some applications to minimax inequalities and variational inequalities. Recently, Ding [3] established some ...

The Reference Point Method (RPM) is an interactive technique for multiple criteria optimization problems. It is based on optimization of the scalarizing achievement function built as the augmented maxmin aggregation of individual outcomes with respect to the given reference levels. Actually, the worst individual achievement is optimized, but regularized with the term representing the average ac...

We study the regret of optimal strategies for online convex optimization games. Using von Neumann’s minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over joint distributions of the adversary’s action sequence, of the difference betwe...

In this paper, a nonlinear phase finite impulse response (FIR) filter is designed without imposing a desired phase response. The maximum passband group delay of the filter is minimized subject to a positivity constraint on the passband group delay response of the filter as well as a specification on the maximum absolute difference between the desired magnitude square response and the designed m...

A weak maximal principle for minimax optimal control problems with mixed state-control equality and inequality constraints is provided. In the formulation of problem we allow parameter uncertainties in all functions involved: cost function, dynamical system constraints. Then a new constraint qualification Mangassarian-Fromovitz type introduced which allowed us to prove necessary conditions opti...