14 citations · 22 across the 9 of their papers we have counts for
9 papers
Moment Relaxations for Data-Driven Wasserstein Distributionally Robust Optimization
Shixuan Zhang, Suhan Zhong
We propose moment relaxations for data-driven -Wasserstein distributionally robust optimization (-WDRO) problems that are defined by polynomials. The proposed moment relaxati…
Semigroups of Integer Points in Convex Cones
Grigoriy Blekherman, Jesús A. De Loera, Luze Xu +1
We study the question whether the affine semigroup of integer points in a convex cone can be finitely generated up to symmetries of the cone. We establish general properties of fin…
Spurious local minima in nonconvex sum-of-squares optimization
Grigoriy Blekherman, Rainer Sinn, Mauricio Velasco +1
We study spurious second-order stationary points and local minima in a nonconvex low-rank formulation of sum-of-squares optimization on a real variety . We reformulate the probl…
Integer Points in Arbitrary Convex Cones: The Case of the PSD and SOC Cones
Jesús A. De Loera, Brittney Marsters, Luze Xu +1
We investigate the semigroup of integer points inside a convex cone. We extend classical results in integer linear programming to integer conic programming. We show that the semigr…
On Distributionally Robust Multistage Convex Optimization: Data-driven Models and Performance
Shixuan Zhang, Xu Andy Sun
This paper presents a novel algorithmic study with extensive numerical experiments of distributionally robust multistage convex optimization (DR-MCO). Following the previous work o…
Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition
Ignacio Aravena, Daniel K. Molzahn, Shixuan Zhang +12
The optimal power flow problem is central to many tasks in the design and operation of electric power grids. This problem seeks the minimum cost operating point for an electric pow…
An ADMM-based Distributed Optimization Method for Solving Security-Constrained AC Optimal Power Flow
Amin Gholami, Kaizhao Sun, Shixuan Zhang +1
In this paper, we study efficient and robust computational methods for solving the security-constrained alternating current optimal power flow (SC-ACOPF) problem, a two-stage nonli…
On Distributionally Robust Multistage Convex Optimization: New Algorithms and Complexity Analysis
Shixuan Zhang, Xu Andy Sun
This paper presents an algorithmic study and complexity analysis for solving distributionally robust multistage convex optimization (DR-MCO) problems. Our main contribution is a no…
Stochastic Dual Dynamic Programming for Multistage Stochastic Mixed-Integer Nonlinear Optimization
Shixuan Zhang, Xu Andy Sun
In this paper, we study multistage stochastic mixed-integer nonlinear programs (MS-MINLP). This general class of problems encompasses, as important special cases, multistage stocha…