We provide motivations for the correlated equilibrium solution concept from the game-theoretic and optimization perspectives. We then propose an algorithm that computes <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\varepsilon}$$</EquationSource> </InlineEquation> -correlated equilibria with global-optimal (i.e., maximum) expected social welfare for normal form...</equationsource></inlineequation>

This paper presents an algorithm and its implementation in the software package <ExternalRef> <RefSource> <Emphasis FontCategory="NonProportional">NCSOStools </RefSource> <RefTarget Address="http://ncsostools.fis.unm.si/" TargetType="URL"/> </ExternalRef> for finding sums of Hermitian squares and commutators decompositions for polynomials in noncommuting variables. The algorithm is based on noncommutative analogs of the classical Gram matrix method and...</emphasis></refsource></externalref>

A basic closed semialgebraic subset of Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb...

We observe that in a simple one-dimensional polynomial optimization problem (POP), the ‘optimal’ values of semidefinite programming (SDP) relaxation problems reported by the standard SDP solvers converge to the optimal value of the POP, while the true optimal values of SDP relaxation...

A semi-definite programming (SDP) formulation of the multi-objective economic-emission dispatch problem is presented. The fuel cost and emission functions are represented by high order polynomial functions and this was shown to be a more accurate representation of the economic-emission dispatch...

We consider polynomial optimization problems pervaded by a sparsity pattern. It has been shown in [1, 2] that the optimal solution of a polynomial programming problem with structured sparsity can be computed by solving a series of semidefinite relaxations that possess the same kind of sparsity....