Related papers: A common parallel framework for LLP combinatorial …
A method is presented for parallelizing the computation of solutions to discrete-time, linear-quadratic, finite-horizon optimal control problems, which we will refer to as LQR problems. This class of problem arises frequently in robotic…
The Simplex tableau has been broadly used and investigated in the industry and academia. With the advent of the big data era, ever larger problems are posed to be solved in ever larger machines whose architecture type did not exist in the…
Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…
In this paper we studied combinatorial problems with parameterized locally budgeted uncertainty. We are looking for a solutions set such that for any parameters vector there exists a solution in the set with robustness near optimal. The…
Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover, a type of integer programming (IP) problem. A lattice-gas model on the Erd\"os-R\'enyi random graphs of $\alpha$-uniform…
This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…
The linear complementarity problem (LCP) is a general set membership problem that includes quadratic cone programming as a special case. In this work we consider a homogeneous embedding of the LCP, which encodes both the optimality…
The combinatorial pricing problem (CPP) is a bilevel problem in which the leader maximizes their revenue by imposing tolls on certain items that they can control. Based on the tolls set by the leader, the follower selects a subset of items…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…
The problem of detecting and removing redundant constraints is fundamental in optimization. We focus on the case of linear programs (LPs) in dictionary form, given by $n$ equality constraints in $n+d$ variables, where the variables are…
We introduce multiple symmetric LP relaxations for minimum cut problems. The relaxations give optimal and approximate solutions when the input is a Hamiltonian cycle. We show that this leads to one of two interesting results. In one case,…
While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient…
In this paper, we present a general framework for efficiently computing diverse solutions to combinatorial optimization problems. Given a problem instance, the goal is to find $k$ solutions that maximize a specified diversity measure; the…
Machine learning has increasingly been employed to solve NP-hard combinatorial optimization problems, resulting in the emergence of neural solvers that demonstrate remarkable performance, even with minimal domain-specific knowledge. To…
In this paper, we consider the problem of scheduling an application on a parallel computational platform. The application is a particular task graph, either a linear chain of tasks, or a set of independent tasks. The platform is made of…
Combinatorial optimization (CO) problems, central to operation research and theoretical computer science, present significant computational challenges due to their NP-hard nature. While large language models (LLMs) have emerged as promising…
A sparse linear programming (SLP) problem is a linear programming problem equipped with a sparsity (or cardinality) constraint, which is nonconvex and discontinuous theoretically and generally NP-hard computationally due to the…
In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
Lazy search algorithms have been developed to efficiently solve planning problems in domains where the computational effort is dominated by the cost of edge evaluation. The existing algorithms operate by intelligently balancing…
Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately.…