Related papers: Exploring the Numerics of Branch-and-Cut for Mixed…
Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized…
The branching algorithm is a fundamental technique for designing fast exponential-time algorithms to solve combinatorial optimization problems exactly. It divides the entire solution space into independent search branches using…
In this paper, we explore statistical versus computational trade-off to address a basic question in the application of a distributed algorithm: what is the minimal computational cost in obtaining statistical optimality? In smoothing spline…
We give an improved branch-and-bound solver for the multiterminal cut problem, based on the recent work of Henzinger et al.. We contribute new, highly effective data reduction rules to transform the graph into a smaller equivalent instance.…
This work attempts to combine the strengths of two major technologies that have matured over the last three decades: global mixed-integer nonlinear optimization and branch-and-price. We consider a class of generally nonconvex mixed-integer…
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…
Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within constraint programming. In…
This paper explores reoptimization techniques for solving sequences of similar mixed integer programs (MIPs) more effectively. Traditionally, these MIPs are solved independently, without capitalizing on information from previously solved…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Given an undirected graph, the k-vertex cut problem (k-VCP) asks for a minimum-cost set of vertices whose removal yields at least k connected components in the resulting graph. The k-VCP is an important problem in network optimization, with…
The branch-and-cut algorithm is the method of choice to solve large scale integer programming problems in practice. A key ingredient of branch-and-cut is the use of cutting planes which are derived constraints that reduce the search space…
Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer…
We study linear programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT), referred to as RLT relaxations. We investigate the relations between the polyhedral properties of the feasible…
A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding…
Large language models (LLMs) have demonstrated exceptional performance not only in natural language processing tasks but also in a great variety of non-linguistic domains. In diverse optimization scenarios, there is also a rising trend of…
Linear programming (LP) relaxations are widely employed in exact solution methods for multilinear programs (MLP). One example is the family of Recursive McCormick Linearization (RML) strategies, where bilinear products are substituted for…
We propose a supervised learning framework for computing solutions of multi-parametric Mixed Integer Linear Programs (MILPs) that arise in Model Predictive Control. Our approach also quantifies sub-optimality for the computed solutions.…
We study numerical integration of smooth functions defined over the $s$-dimensional unit cube. A recent work by Dick et al. (2019) has introduced so-called extrapolated polynomial lattice rules, which achieve the almost optimal rate of…
Integer Linear Programming (ILP) formulations of Markov random fields (MRFs) models with global connectivity priors were investigated previously in computer vision, e.g., \cite{globalinter,globalconn}. In these works, only Linear Programing…
Combinatorial optimisation problems framed as mixed integer linear programmes (MILPs) are ubiquitous across a range of real-world applications. The canonical branch-and-bound algorithm seeks to exactly solve MILPs by constructing a search…