相关论文: Basis Reduction, and the Complexity of Branch-and-…

The submodular function maximization is an attractive optimization model that appears in many real applications. Although a variety of greedy algorithms quickly find good feasible solutions for many instances while guaranteeing…

This paper presents and evaluates two pruning techniques to reinforce the efficiency of constraint optimization solvers based on multi-valued decision-diagrams (MDD). It adopts the branch-and-bound framework proposed by Bergman et al. in…

In bi-objective integer optimization the optimal result corresponds to a set of non-dominated solutions. We propose a generic bi-objective branch-and-bound algorithm that uses a problem-independent branching rule exploiting available…

Data-driven algorithm design is a paradigm that uses statistical and machine learning techniques to select from a class of algorithms for a computational problem an algorithm that has the best expected performance with respect to some…

We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…

In this paper we explore a relevant aspect of the interplay between two core elements of global optimization algorithms for nonconvex nonlinear programming problems, which we believe has been overlooked by past literature. The first one is…

The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To…

Given a graph $G=(V,E)$, the minimum branch vertices problem consists in finding a spanning tree $T=(V,E')$ of $G$ minimizing the number of vertices with degree greater than two. We consider a simple combinatorial lower bound for the…

Since the breakthrough superpolynomial multilinear formula lower bounds of Raz (Theory of Computing 2006), proving such lower bounds against multilinear algebraic branching programs (mABPs) has been a longstanding open problem in algebraic…

Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A. Necessary and sufficient conditions for the exact computation of AA^T (in exact arithmetic) from c…

We analyse the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We derive new tighter deterministic and probabilistic bounds that we use to…

We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is…

We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…

Rank-constrained matrix problems appear frequently across science and engineering. The convergence analysis of iterative algorithms developed for these problems often hinges on local error bounds, which correlate the distance to the…

Deterministic computer simulations are often used as a replacement for complex physical experiments. Although less expensive than physical experimentation, computer codes can still be time-consuming to run. An effective strategy for…

Machine learning is increasingly used to guide branch-and-cut (B&C) for mixed-integer linear programming by learning score-based policies for selecting branching variables and cutting planes. Many approaches train on local signals from…

Minimum Spanning Trees are a well-studied subset of graph problems. While classical algorithms have existed to solve these problems for decades, new variations and application areas are constantly being discovered. When dealing with large…

State-of-the-art branch and bound algorithms for mixed integer programming make use of special methods for making branching decisions. Strategies that have gained prominence include modern variants of so-called strong branching (Applegate,…

We present a generic branch-and-bound algorithm for finding all the Pareto solutions of a biobjective mixed-integer linear program. The main contributions are new algorithms for obtaining dual bounds at a node, for checking node fathoming,…

We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…