Abstract This paper studies convex generalized Nash equilibrium problems that are given by polynomials. We use rational and parametric expressions for Lagrange multipliers to formulate efficient polynomial optimization computing equilibria (GNEs). The Moment-SOS hierarchy of semidefinite relaxations used solve the optimization. Under some general assumptions, we prove method can find a GNE if t...

Domain theory has been used with great success in providing a semantic framework for Turing computability, over both discrete and continuous spaces. On the other hand, classical approximation theory provides a rich set of tools for computations over real functions with (mainly) polynomial and rational function approximations. We present a semantic model for computations over real functions base...

About one class polynomial problems with not polynomial certificates Kochkarev B.S. Abstract. We build a class of polynomial problems with not polynomial certificates. The parameter concerning which are defined efficiency of corresponding algorithms is the number n of elements of the set has used at construction of combinatory objects (families of subsets) with necessary properties. Let Σ = {0,...

We present a new method for solving the hidden polynomial graph problem (HPGP) which is a special case of the hidden polynomial problem (HPP). The new approach yields an efficient quantum algorithm for the bivariate HPGP even when the input consists of several level set superpositions, a more difficult version of the problem than the one where the input is given by an oracle. For constant degre...