Related papers: Linear Programming Relaxations of Quadratically Co…
This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…
We consider linear and semidefinite programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT relaxation), and the Shor relaxation combined with the RLT relaxation (SDP-RLT relaxation).…
We prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints as it has been proposed by Liberti in 2007. The new conditions…
This paper addresses the optimal covariance steering problem for stochastic discrete-time linear systems subject to probabilistic state and control constraints. A method is presented for efficiently attaining the exact solution of the…
We develop a general framework for finding approximately-optimal preconditioners for solving linear systems. Leveraging this framework we obtain improved runtimes for fundamental preconditioning and linear system solving problems including…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
Globally optimizing a nonconvex quadratic over the intersection of $m$ balls in $\mathbb{R}^n$ is known to be polynomial-time solvable for fixed $m$. Moreover, when $m=1$, the standard semidefinite relaxation is exact. When $m=2$, it has…
Recent advances in the efficiency and robustness of algorithms solving convex quadratically constrained quadratic programming (QCQP) problems motivate developing techniques for creating convex quadratic relaxations that, although more…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
This note proposes a new reformulation of complex semidefinite programs (SDPs) as real SDPs. As an application, we present an economical reformulation of complex SDP relaxations of complex polynomial optimization problems as real SDPs and…
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…
This paper formulates a semidefinite programming relaxation for a long horizon direct-torque finite-control-set model predictive control problem. In parallel with this relaxation, a conventional branch-and-bound algorithm tailored for the…
Mathematical programs with complementarity constraints are notoriously difficult to solve due to their nonconvexity and lack of constraint qualifications in every feasible point. This work focuses on the subclass of quadratic programs with…
The reformulation-linearization technique (RLT) is a prominent approach to constructing tight linear relaxations of non-convex continuous and mixed-integer optimization problems. The goal of this paper is to extend the applicability and…
This paper studies how to compute global minimizers of the cubic-quartic regularization (CQR) problem \[ \min_{s \in \mathbb{R}^n} \quad f_0+g^Ts+\frac{1}{2}s^THs+\frac{\beta}{6} \| s \|^3+\frac{\sigma}{4} \| s \|^4, \] where $f_0$ is a…
This paper presents a new approach to quadrify a polynomial programming problem, i.e. reduce the polynomial program to a quadratic program, before solving it. The proposed approach, QUAD-RLT, exploits the Reformulation-Linearization…
This paper explores a new class of constrained difference programming problems, where the objective and constraints are formulated as differences of functions, without requiring their convexity. To investigate such problems, novel variants…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
This paper begins with a class of convex quadratic programs (QPs) with bounded variables solvable by the parametric principal pivoting algorithm with $\mathcal{O}(n^3)$ strongly polynomial complexity, where $n$ is the number of variables of…
A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…