The graph partition problem is the problem of partitioning the vertex set of a graph into a fixed number of sets of given sizes such that the total weight of edges joining different sets is optimized. In this paper we simplify a known matrix-lifting semidefinite programming relaxation of the graph partition problem for several classes of graphs and also show how to aggregate additional triangle...

In this paper, we study a class of biquadratic optimization problems. We first relax the original problem to its semidefinite programming (SDP) problem and discuss the approximation ratio between them. Under some conditions, we show that the relaxed problem is tight. Then we consider how to approximately solve the problems in polynomial time. Under several different constraints, we present vari...

We address the issue of computing a global minimizer AC Optimal Power Flow problem. introduce valid inequalities to strengthen Semidefinite Programming relaxation, yielding novel Conic relaxation. Leveraging these constraints, we dynamically generate Mixed-Integer Linear (MILP) relaxations, whose solutions asymptotically converge minimizers apply this iterative MILP scheme on IEEE PES PGLib [2]...

Abstract. Consider N points in Rd and M local coordinate systems that are related through unknown rigid transforms. For each point we are given (possibly noisy) measurements of its local coordinates in some of the coordinate systems. Alternatively, for each coordinate system, we observe the coordinates of a subset of the points. The problem of estimating the global coordinates of the N points (...

The class of POPs (Polynomial Optimization Problems) over cones covers a wide range of optimization problems such as 0-1 integer linear and quadratic programs, nonconvex quadratic programs and bilinear matrix inequalities. This paper presents a new framework for convex relaxation of POPs over cones in terms of linear optimization problems over cones. It provides a unified treatment of many exis...

Nonconvex Quadratic Optimization, Semidefinite Relaxation, and Applications Zhi-Quan Luo, Wing-Kin Ma, Anthony Man-Cho So, Yinyu Ye, and Shuzhong Zhang 1 Department of Electrical and Computer Engineering, University of Minnesota, MN, USA 2 Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 3 Department of Systems Engineering and Engineering Management, The Chin...