3 citations · 4 across the 15 of their papers we have counts for
18 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…
A Tight SDP Relaxation for the Cubic-Quartic Regularization Problem
Jinling Zhou, Xin Liu, Jiawang Nie +1
This paper studies how to compute global minimizers of the cubic-quartic regularization (CQR) problem \[ \min_{s \in \mathbb{R}^n} \quad f_0+g^Ts+\frac{1}{2}s^THs+\fracβ{6}\| s \|^…
Robust Completion for Rank-1 Tensors with Noises
Jiawang Nie, Xindong Tang, Jinling Zhou
This paper studies the rank-1 tensor completion problem for cubic tensors when there are noises for observed tensor entries. First, we propose a robust biquadratic optimization mod…
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…
A Characterization for Tightness of the Sparse Moment-SOS Hierarchy
Jiawang Nie, Zheng Qu, Xindong Tang +1
This paper studies the sparse Moment-SOS hierarchy of relaxations for solving sparse polynomial optimization problems. We show that this sparse hierarchy is tight if and only if th…
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…
Geometry-Aware Safety-Critical Local Reactive Controller for Robot Navigation in Unknown and Cluttered Environments
Yulin Li, Xindong Tang, Kai Chen +3
This work proposes a safety-critical local reactive controller that enables the robot to navigate in unknown and cluttered environments. In particular, the trajectory tracking task…
Solving polynomial variational inequality problems via Lagrange multiplier expressions and Moment-SOS relaxations
Jiawang Nie, Defeng Sun, Xindong Tang +1
In this paper, we study variational inequality problems (VIPs) with involved mappings and feasible sets characterized by polynomial functions (namely, polynomial VIPs). We propose…
A Correlatively Sparse Lagrange Multiplier Expression Relaxation for Polynomial Optimization
Zheng Qu, Xindong Tang
In this paper, we consider polynomial optimization with correlative sparsity. We construct correlatively sparse Lagrange multiplier expressions (CS-LMEs) and propose CS-LME reformu…
On the polyhedral homotopy method for solving generalized Nash equilibrium problems of polynomials
Kisun Lee, Xindong Tang
The generalized Nash equilibrium problem (GNEP) is a kind of game to find strategies for a group of players such that each player's objective function is optimized. Solutions for G…
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…
Dehomogenization for Completely Positive Tensors
Jiawang Nie, Xindong Tang, Zi Yang +1
A real symmetric tensor is completely positive (CP) if it is a sum of symmetric tensor powers of nonnegative vectors. We propose a dehomogenization approach for studying CP tensors…
Rational Generalized Nash Equilibrium Problems
Jiawang Nie, Xindong Tang, Suhan Zhong
This paper studies generalized Nash equilibrium problems that are given by rational functions. The optimization problems are not assumed to be convex. Rational expressions for Lagr…
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…
Nash Equilibrium Problems of Polynomials
Jiawang Nie, Xindong Tang
This paper studies Nash equilibrium problems that are given by polynomial functions. We formulate efficient polynomial optimization problems for computing Nash equilibria. The Lass…