6 papers
Sparse Copositive Polynomial Optimization
Suhan Zhong, Jinling Zhou, Jiawang Nie +1
This paper studies the copositive optimization problem whose objective is a sparse polynomial, with linear constraints over the nonnegative orthant. We propose sparse Moment-SOS re…
Max-Min Bilinear Completely Positive Programs: A Semidefinite Relaxation with Tightness Guarantees
Sarah Yini Gao, Xindong Tang, Yancheng Yuan
Max-min bilinear optimization models, where one agent maximizes and an adversary minimizes a common bilinear objective, serve as canonical saddle-point formulations in optimization…
Log-Polynomial Optimization
Jiyoung Choi, Jiawang Nie, Xindong Tang +1
We study an optimization problem in which the objective is given as a sum of logarithmic-polynomial functions. This formulation is motivated by statistical estimation principles su…
Sparse Polynomial Optimization with Matrix Constraints
Jiawang Nie, Zheng Qu, Xindong Tang +1
This paper studies the hierarchy of sparse matrix Moment-SOS relaxations for solving sparse polynomial optimization problems with matrix constraints. First, we prove a sufficient a…
Convex Generalized Nash Equilibrium Problems and Polynomial Optimization
Jiawang Nie, Xindong Tang
This paper studies convex Generalized Nash Equilibrium Problems (GNEPs) that are given by polynomials. We use rational and parametric expressions for Lagrange multipliers to formul…
The Gauss-Seidel Method for Generalized Nash Equilibrium Problems of Polynomials
Jiawang Nie, Xindong Tang, Lingling Xu
This paper concerns the generalized Nash equilibrium problem of polynomials (GNEPP). We apply the Gauss-Seidel method and Lasserre type Moment-SOS relaxations to solve GNEPPs. The…