Related papers: Linear Programming Relaxations of Quadratically Co…
The current bottleneck of globally solving mixed-integer (non-convex) quadratically constrained problem (MIQCP) is still to construct strong but computationally cheap convex relaxations, especially when dense quadratic functions are…
We consider the nonlinear integer programming problem of minimizing a quadratic function over the integer points in variable dimension satisfying a system of linear inequalities. We show that when the Graver basis of the matrix defining the…
We consider the problem of computing the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints that admit quadratic relaxations. These non-convex constraints include semialgebraic sets and other…
Computational equilibrium finding in large zero-sum extensive-form imperfect-information games has led to significant recent AI breakthroughs. The fastest algorithms for the problem are new forms of counterfactual regret minimization [Brown…
Semidefinite programming is an indispensable tool in computer vision, but general-purpose solvers for semidefinite programs are often too slow and memory intensive for large-scale problems. We propose a general framework to approximately…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…
The linear programming method is applied to the space $\U_n(\C)$ of unitary matrices in order to obtain bounds for codes relative to the diversity sum and the diversity product. Theoretical and numerical results improving previously known…
Finite linear least squares is one of the core problems of numerical linear algebra, with countless applications across science and engineering. Consequently, there is a rich and ongoing literature on algorithms for solving linear least…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \sum_{i \ne j} a_{ij} x_i x_j. QP captures many known combinatorial optimization problems, and assuming the unique games conjecture,…
Nonlinear matrix equations arise in many practical contexts related to control theory, dynamical programming and finite element methods for solving some partial differential equations. In most of these applications, it is needed to compute…
Linear programs with quadratic regularization are attracting renewed interest due to their applications in optimal transport: unlike entropic regularization, the squared-norm penalty gives rise to sparse approximations of optimal transport…
Parametric linear programming is central in polyhedral computations and in certain control applications.We propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.
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…
In this paper, we study a class of fractional semi-infinite polynomial programming problems involving s.o.s-convex polynomial functions. For such a problem, by a conic reformulation proposed in our previous work and the quadratic modules…
In this paper we study the Shor relaxation of quadratic programs by fixing a feasible set and considering the space of objective functions for which the Shor relaxation is exact. We first give conditions under which this region is invariant…
Sparsity is a fundamental modeling principle in statistics, signal processing, and data science. However, optimization with sparsity constraints is notoriously difficult. We introduce a new convex relaxation framework for {sparse…
Bounding the correlations predicted by quantum theory is an important challenge in quantum information science. Today's leading approach is semidefinite programming relaxations, but existing methods still cannot account for many relevant…
This paper provides the first meaningful documentation and analysis of an established technique which aims to obtain an approximate solution to linear programming problems prior to applying the primal simplex method. The underlying…