Related papers: A Computational Study of Perspective Cuts
Current state-of-the-art methods for solving discrete optimization problems are usually restricted to convex settings. In this paper, we propose a general approach based on cutting planes for solving nonlinear, possibly nonconvex, binary…
We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that combining cutting planes and branching into a branch-and-cut…
Branch and cut is the dominant paradigm for solving a wide range of mathematical programming problems -- linear or nonlinear -- combining efficient search (via branch and bound) and relaxation-tightening procedures (via cutting planes, or…
Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of…
Cutting planes are a key ingredient to successfully solve mixed-integer linear programs. For specific problems, their strength is often theoretically assessed by showing that they are facet-defining for the corresponding mixed-integer hull.…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
Our study is motivated by the solution of Mixed-Integer Non-Linear Programming (MINLP) problems with separable non-convex functions via the Sequential Convex MINLP technique, an iterative method whose main characteristic is that of solving,…
Cutting plane methods are a fundamental approach for solving integer linear programs (ILPs). In each iteration of such methods, additional linear constraints (cuts) are introduced to the constraint set with the aim of excluding the previous…
Cutting planes are of crucial importance when solving nonconvex nonlinear programs to global optimality, for example using the spatial branch-and-bound algorithms. In this paper, we discuss the generation of cutting planes for signomial…
This paper studies disjunctive cutting planes in Mixed-Integer Conic Programming. Building on conic duality, we formulate a cut-generating conic program for separating disjunctive cuts, and investigate the impact of the normalization…
We study the generalization of split, k-branch split, and intersection cuts from Mixed Integer Linear Programming to the realm of Mixed Integer Nonlinear Programming. Constructing such cuts requires calculating the convex hull of the…
Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter…
Cutting plane methods, particularly outer approximation, are a well-established approach for solving nonlinear discrete optimization problems without relaxing the integrality of decision variables. While powerful in theory, their…
Cutting plane methods play a significant role in modern solvers for tackling mixed-integer programming (MIP) problems. Proper selection of cuts would remove infeasible solutions in the early stage, thus largely reducing the computational…
We consider the global optimization of nonconvex mixed-integer quadratic programs with linear equality constraints. In particular, we present a new class of convex quadratic relaxations which are derived via quadratic cuts. To construct…
We present a geometrical analysis on the completely positive programming reformulation of quadratic optimization problems and its extension to polynomial optimization problems with a class of geometrically defined nonconvex conic programs…
We survey recent work on machine learning (ML) techniques for selecting cutting planes (or cuts) in mixed-integer linear programming (MILP). Despite the availability of various classes of cuts, the task of choosing a set of cuts to add to…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…