Related papers: Cutting-plane methods witout nested approximating …
The incorporation of cutting planes within the branch-and-bound algorithm, known as branch-and-cut, forms the backbone of modern integer programming solvers. These solvers are the foremost method for solving discrete optimization problems…
This paper develops the proximal method of multipliers for a class of nonsmooth convex optimization. The method generates a sequence of minimization problems (subproblems). We show that the sequence of approximations to the solutions of the…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
Whether it is object detection, model reconstruction, laser odometry, or point cloud registration: Plane extraction is a vital component of many robotic systems. In this paper, we propose a strictly probabilistic method to detect finite…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…
This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal…
In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
Machine learning develops rapidly, which has made many theoretical breakthroughs and is widely applied in various fields. Optimization, as an important part of machine learning, has attracted much attention of researchers. With the…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…
Residuation theory concerns the study of partially ordered algebraic structures, most often monoids, equipped with a weak inverse for the monoidal operator. One of its area of application has been constraint programming, whose key…
Tree decompositions were developed by Robertson and Seymour. Since then algorithms have been developed to solve intractable problems efficiently for graphs of bounded treewidth. In this paper we extend tree decompositions to allow cycles to…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
Outer approximation methods have long been employed to tackle a variety of optimization problems, including linear programming, in the 1960s, and continue to be effective for solving variational inequalities, general convex problems, as…
We introduce and study Minimum Cut Representability, a framework to solve optimization and feasibility problems over stable matchings by representing them as minimum s-t cut problems on digraphs over rotations. We provide necessary and…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
Linear programming is the seminal optimization problem that has spawned and grown into today's rich and diverse optimization modeling and algorithmic landscape. This article provides an overview of the recent development of first-order…