In this paper, we propose a primal interior-point method for large sparse generalized minimax optimization. After a short introduction, where the problem is stated, we introduce the basic equations of the Newton method applied to the KKT conditions and propose a primal interior-point method. (i. e. interior point method that uses explicitly computed approximations of Lagrange multipliers instead of their updates). Next we describe the basic algorithm and give more details concerning its implementation...

In this paper, we propose a primal interior-point method for large sparse minimax optimization. After a short introduction, the complete algorithm is introduced and important implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Thus the large sparse nonconvex minimax optimization problems can be solved successfully. The results of extensive computational experiments given in this paper confirm efficiency and robustness of the proposed...

Considered here are production (or market) games with transferable utility. Prime objects are explicitly computable core solutions, or somewhat "deficit" versions of such, fully defined by shadow prices. Main arguments revolve around standard Lagrangian duality. A chief concern is to relax, or avoid, the commonplace assumption that all preferences and production possibilities be convex. Doing so, novel results are obtained about non-emptiness of the core, and about specific imputations therein.