相关论文: Extended Triangle Inequalities for Nonconvex Box-C…

It has recently been shown (Burer, Math. Program Ser. A 120:479-495, 2009) that a large class of NP-hard nonconvex quadratic programming problems can be modeled as so called completely positive programming problems, which are convex but…

Polynomial optimization encompasses a broad class of problems in which both the objective function and constraints are polynomial functions of the decision variables. In recent years, a substantial body of research has focused on…

This two-part paper is concerned with the problem of minimizing a linear objective function subject to a bilinear matrix inequality (BMI) constraint. In this part, we first consider a family of convex relaxations which transform BMI…

We investigate the possibility of solving continuous non-convex optimization problems using a network of interacting quantum optical oscillators. We propose a native encoding of continuous variables in analog signals associated with the…

We investigate new convex relaxations for the pooling problem, a classic nonconvex production planning problem in which input materials are mixed in intermediate pools, with the outputs of these pools further mixed to make output products…

Random constraint satisfaction problems (CSPs) such as random $3$-SAT are conjectured to be computationally intractable. The average case hardness of random $3$-SAT and other CSPs has broad and far-reaching implications on problems in…

Classical existence theorems and solution methods for quadratic programming traditionally rely on the analytical properties of real numbers, specifically compactness and completeness. These tools are unavailable in general linearly ordered…

Quantum computing has emerged as a promising alternative for solving combinatorial optimization problems. The standard approach for encoding optimization problems on quantum processing units (QPUs) involves transforming them into their…

There has been growing interest in high-order tensor methods for nonconvex optimization, with adaptive regularization, as they possess better/optimal worst-case evaluation complexity globally and faster convergence asymptotically. These…

Boolean quadratic optimization problems occur in a number of applications. Their mixed integer-continuous nature is challenging, since it is inherently NP-hard. For this motivation, semidefinite programming relaxations (SDR's) are proposed…

Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…

A subset of Q^n is called semilinear (or piecewise linear) if it is Boolean combination of linear half-spaces. We study the computational complexity of the constraint satisfaction problem (CSP) over the rationals when all the constraints…

We have recently presented a method to solve an overdetermined linear system of equations with multiple right hand side vectors, where the unknown matrix is to be symmetric and positive definite. The coefficient and the right hand side…

We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. In…

We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression,…

Semidefinite programming (SDP) relaxations have been intensively used for solving discrete quadratic optimization problems, in particular in the binary case. For the general non-convex integer case with box constraints, the branch-and-bound…

We develop tractable convex relaxations for rank-constrained quadratic optimization problems over $n \times m$ matrices, a setting for which tractable relaxations are typically only available when the objective or constraints admit spectral…

The worst-case robust adaptive beamforming problem for general-rank signal model is considered. This is a nonconvex problem, and an approximate version of it (obtained by introducing a matrix decomposition on the presumed covariance matrix…

A novel algorithm to solve the quadratic programming problem over ellipsoids is proposed. This is achieved by splitting the problem into two optimisation sub-problems, quadratic programming over a sphere and orthogonal projection. Next, an…

One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well-known McCormick relaxation for a product of two variables x and y over a box-constrained domain. The starting point of this paper is the fact…