相关论文: k-Disjunctive cuts and a finite cutting plane algo…

An important problem in optimization is the construction of mixed-integer programming (MIP) formulations of disjunctive constraints that are both strong and small. Motivated by lower bounds on the number of integer variables that are…

Linear bilevel programs (linear BLPs) have been widely used in computational mathematics and optimization in several applications. Single-level reformulation for linear BLPs replaces the lower-level linear program with its…

This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…

In this paper, we present a novel algorithm for piecewise linear regression which can learn continuous as well as discontinuous piecewise linear functions. The main idea is to repeatedly partition the data and learn a liner model in in each…

Generalized Disjunctive Programming (GDP) provides a powerful framework for combining algebraic constraints with logical disjunctions. To solve these problems, mixed-integer reformulations are required, but traditional reformulation…

Balas introduced disjunctive cuts in the 1970s for mixed-integer linear programs. Several recent papers have attempted to extend this work to mixed-integer conic programs. In this paper we study the structure of the convex hull of a…

In this paper, we present a method to determine if a lift-and-project cut for a mixed-integer linear program is irregular, in which case the cut is not equivalent to any intersection cut from the bases of the linear relaxation. This is an…

An analytic center cutting plane method is an iterative algorithm based on the computation of analytic centers. In this paper, we propose some analytic center cutting plane methods for solving quasimonotone or pseudomonotone variational…

Graph separation is a central tool in parameterized algorithm design, and important separators are among its most successful ingredients. They yield small, structured families of separators that can be enumerated efficiently, and underlie…

In computer algebra there are different ways of approaching the mathematical concept of functions, one of which is by defining them as solutions of differential equations. We compare different such approaches and discuss the occurring…

We introduce a stochastic version of the cutting-plane method for a large class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems. We show that under very weak assumptions the stochastic algorithm is able to converge to…

This paper studies bilevel polynomial optimization in which lower-level constraint functions depend linearly on lower-level variables. We show that such bilevel program can be reformulated as a disjunctive program by using…

This paper investigates linear programming based branch-and-bound using general disjunctions, also known as stabbing planes, for solving integer programs. We derive the first sub-exponential lower bound (in the encoding length $L$ of the…

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…

In this paper, we study a class of nonconvex and nonsmooth structured difference-of-convex (DC) programs, which contain in the convex part the sum of a nonsmooth linearly composed convex function and a differentiable function, and in the…

Given an undirected, edge-weighted graph G together with pairs of vertices, called pairs of terminals, the minimum multicut problem asks for a minimum-weight set of edges such that, after deleting these edges, the two terminals of each pair…

Cutting planes are essential for solving mixed-integer linear problems (MILPs), because they facilitate bound improvements on the optimal solution value. For selecting cuts, modern solvers rely on manually designed heuristics that are tuned…

We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set…

This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated,…

Mixed-integer rounding (MIR) cutting planes (cuts) are effective at improving the strength of a linear relaxation for mixed-integer linear programming (MIP) problems. The cuts in this family are derived by aggregating constraints then…