Related papers: Tight-and-cheap conic relaxation for the AC optima…
This paper studies an optimization problem on the sum of traces of matrix quadratic forms in $m$ semi-orthogonal matrices, which can be considered as a generalization of the synchronization of rotations. While the problem is nonconvex, the…
Alternating current optimal power flow (AC OPF) is one of the most fundamental optimization problems in electrical power systems. It can be formulated as a semidefinite program (SDP) with rank constraints. Solving AC OPF, that is, obtaining…
This paper deals with the non-convex power system state estimation (PSSE) problem, which plays a central role in the monitoring and operation of electric power networks. Given a set of noisy measurements, PSSE aims at estimating the vector…
Combined heat and power dispatch promotes interactions and synergies between electric power systems and district heating systems. However, nonlinear and nonconvex heating flow imposes significant challenges on finding qualified solutions…
Mixed-Integer Quadratically Constrained Quadratic Programs arise in a variety of applications, particularly in energy, water, and gas systems, where discrete decisions interact with nonconvex quadratic constraints. These problems are…
Power system operators are increasingly deploying Variable Impedance Devices (VIDs), e.g., Smart Wires, and Network Topology Optimization (NTO) schemes for mitigating operational challenges such as line and transformer congestion, and…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
Optimizing a nonlinear function over nonconvex sets is challenging since solving convex relaxations may lead to substantial relaxation gaps and infeasible solutions that must be "rounded" to feasible ones, often with uncontrollable losses…
We extend the convergence analysis for methods solving PDE-constrained optimal control problems containing both discrete and continuous control decisions based on relaxation and rounding strategies to the class of first order semilinear…
The classical $\textit{Procrustes}$ problem is to find a rigid motion (orthogonal transformation and translation) that best aligns two given point-sets in the least-squares sense. The $\textit{Robust Procrustes}$ problem is an important…
The problem of minimizing a (nonconvex) quadratic form over the unit simplex, referred to as a standard quadratic program, admits an exact convex conic formulation over the computationally intractable cone of completely positive matrices.…
In this paper, by improving the variable-splitting approach, we propose a new semidefinite programming (SDP) relaxation for the nonconvex quadratic optimization problem over the $\ell_1$ unit ball (QPL1). It dominates the state-of-the-art…
In this letter, we present an alternative mixed-integer non-liner programming formulation of the reactive optimal power flow (ROPF) problem. We utilize a mixed-integer second-order cone programming (MISOCP) based approach to find global…
The uncertainty of multiple power loads and renewable energy generations (PLREG) in power systems increases the complexity of power flow analysis for decision-makers. The chance-constrained method can be applied to model the optimization…
Tight convex and concave relaxations are of high importance in the field of deterministic global optimization. We present a heuristic to tighten relaxations obtained by the McCormick technique. We use the McCormick subgradient propagation…
This article presents a new method for computing guaranteed convex and concave relaxations of nonlinear stochastic optimal control problems with final-time expected-value cost functions. This method is motivated by similar methods for…
This paper proposes a general fixture layout design framework that directly integrates the system equation with the convex relaxation method. Note that the optimal fixture design problem is a large-scale combinatorial optimization problem,…
We propose a branch flow model for the anal- ysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates…
Many high dimensional sparse learning problems are formulated as nonconvex optimization. A popular approach to solve these nonconvex optimization problems is through convex relaxations such as linear and semidefinite programming. In this…
We propose a method for low-rank semidefinite programming in application to the semidefinite relaxation of unconstrained binary quadratic problems. The method improves an existing solution of the semidefinite programming relaxation to…