4 papers
Algebraic Degrees of Generalized Nash Equilibrium Problems
Jiawang Nie, Kristian Ranestad, Xindong Tang
This paper studies the algebraic degree of generalized Nash equilibrium problems (GNEPs) given by polynomials. Their generalized Nash equilibria (GNEs), as well as their KKT or Fri…
Partial Lagrange Multiplier Expressions and Disjunctive Decompositions for Bilevel Optimization
Jiawang Nie, Jane J. Ye, Suhan Zhong
This paper studies bilevel polynomial optimization in which lower-level constraint functions depend linearly on lower-level variables. We show that such bilevel program can be refo…
Distributionally Robust Optimization with Polynomial Robust Constraints
Jiawang Nie, Suhan Zhong
This paper studies distributionally robust optimization (DRO) with polynomial robust constraints. We give a Moment-SOS relaxation approach to solve the DRO. This reduces to solving…
Polynomial Optimization Relaxations for Generalized Semi-Infinite Programs
Xiaomeng Hu, Jiawang Nie
This paper studies generalized semi-infinite programs (GSIPs) given by polynomials. We propose a hierarchy of polynomial optimization relaxations to solve them. They are based on L…