Related papers: Consistency Cuts for Dantzig-Wolfe Reformulations
An optimization problem considering AC power flow constraints and integer decision variables can usually be posed as a mixed-integer quadratically constrained quadratic program (MIQCQP) problem. In this paper, first, a set of valid linear…
This paper describes a new approach on optimization of constraint satisfaction problems (CSPs) by means of substituting sub-CSPs with locally consistent regular membership constraints. The purpose of this approach is to reduce the number of…
We present a new formulation based on the classical Dirichlet-Neumann formulation for interface coupling problems in linearized elasticity. By using Taylor series expansions, we derive a new set of interface conditions that allow our…
We focus on the convergence analysis of averaged relaxations of cutters, specifically for variants that---depending upon how parameters are chosen---resemble \emph{alternating projections}, the \emph{Douglas--Rachford method}, \emph{relaxed…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…
We introduce and study a novel generalization of the classical Knapsack Problem (KP), called the Colored Knapsack Problem (CKP). In this problem, the items are partitioned into classes of colors and the packed items need to be ordered such…
Solving a system of nonlinear inequalities is an important problem for which conventional numerical analysis has no satisfactory method. With a box-consistency algorithm one can compute a cover for the solution set to arbitrarily close…
We provide a simple, general argument to obtain improvements of concentration-type inequalities starting from improvements of their corresponding isoperimetric-type inequalities. We apply this argument to obtain robust improvements of the…
We study the integrality gap of convex mixed-integer programs, that is, the difference between the optimal value of such a problem and the optimal value of its continuous relaxation. We study classes of convex sets whose associated…
Dantzig selector (DS) and LASSO problems have attracted plenty of attention in statistical learning, sparse data recovery and mathematical optimization. In this paper, we provide a theoretical analysis of the sparse recovery stability of…
Despite strong performance on a variety of tasks, neural sequence models trained with maximum likelihood have been shown to exhibit issues such as length bias and degenerate repetition. We study the related issue of receiving…
We present a pure linear cutting-plane relaxation approach for rapidly proving tight and accurate lower bounds for the Alternating Current Optimal Power Flow Problem (ACOPF) and its multi-period extension with ramping constraints. Our…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
We analyze the preservation properties of a family of reversible splitting methods when they are applied to the numerical time integration of linear differential equations defined in the unitary group. The schemes involve complex…
We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…
The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical…
We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate…
We present a new Frank-Wolfe (FW) type algorithm that is applicable to minimization problems with a nonsmooth convex objective. We provide convergence bounds and show that the scheme yields so-called coreset results for various Machine…
In this paper, we propose first-order feasible methods for difference-of-convex (DC) programs with smooth inequality and simple geometric constraints. Our strategy for maintaining feasibility of the iterates is based on a "retraction" idea…
In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they…