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…
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…
A global approach for generalized semi-infinte programs with polyhedral parameter sets
Xiaomeng Hu, Jiawang Nie, Suhan Zhong
This paper studies generalized semi-infinite programs (GSIPs) defined with polyhedral parameter sets. Assume these GSIPs are given by polynomials. We propose a new approach to solv…
Positivstellensätze and Moment problems with Universal Quantifiers
Xiaomeng Hu, Igor Klep, Jiawang Nie
This paper studies Positivstellensätze and moment problems for sets that are given by universal quantifiers. Let be a closed set and let be a tuple of…
Generalized Nash equilibrium problems with quasi-linear constraints
Jiyoung Choi, Jiawang Nie, Xindong Tang +1
We study generalized Nash equilibrium problems (GNEPs) such that objectives are polynomial functions, and each player's constraints are linear in their own strategy. For such GNEPs…
Towards Global Solutions for Nonconvex Two-Stage Stochastic Programs: A Polynomial Lower Approximation Approach
Suhan Zhong, Ying Cui, Jiawang Nie
This paper tackles the challenging problem of finding global optimal solutions for two-stage stochastic programs with continuous decision variables and nonconvex recourse functions…