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...

In the present work, under some di¤erentiability conditions on the potential functions , we …rst reduce the inverse scattering problem (ISP) for the polynomial pencil of the Scroedinger equation to the corresponding ISP for the generalized matrix Scrödinger equation . Then ISP will be solved in analogy of the Marchenko method. We aim to establish an e¤ective algorithm for uniquely reconstructin...

In this paper, we develop an optimization-based approach to multivariate Chebyshev approximation on a finite grid. We consider two models: polynomial and generalized rational approximation. the second case, approximations are ratios of linear forms basis functions not limited monomials. It is already known that in case grid corresponding optimization problems can be reduced solving programming ...