Decomposition approaches can be used to generate practically efficient solution algorithms for a wide class of optimization problems. For instance, scenario-expanded two-stage stochastic optimization problems can be solved efficiently in practice using Benders Decomposition. The performance of the approach can be influenced by the choice of the cuts that are added during the course of … Read more
In the Subspace Clustering with Missing Data (SCMD) problem, we are given a collection of n partially observed d-dimensional vectors. The data points are assumed to be concentrated near a union of low-dimensional subspaces. The goal of SCMD is to cluster the vectors according to their subspace membership and recover the underlying basis, which can … Read more
Problem definition: We study the problem of designing large-scale resilient relay logistics hub networks. We propose a model of k-Shortest Path Network Design, which aims to improve a network’s efficiency and resilience through its topological configuration, by locating relay logistics hubs to connect each origin-destination pair with k paths of minimum lengths, weighted by their … Read more
Regularization by the Shannon entropy enables us to efficiently and approximately solve optimal transport problems on a finite set. This paper is concerned with regularized optimal transport problems via Bregman divergence. We introduce the required properties for Bregman divergences, provide a non-asymptotic error estimate for the regularized problem, and show that the error estimate becomes … Read more
We study a class of nonlinear optimization problems with diverse practical applications, particularly in cooperative game theory. These problems are referred to as Maximum Multiplicative Programs (MMPs), and can be conceived as instances of “Optimization Over the Frontier” in multiobjective optimization. To solve MMPs, we introduce a feasibility pump-based heuristic that is specifically designed to … Read more
Recently Grimmer [1] showed for smooth convex optimization by utilizing longer steps periodically, gradient descent’s state-of-the-art O(1/T) convergence guarantees can be improved by constant factors, conjecturing an accelerated rate strictly faster than O(1/T) could be possible. Here we prove such a big-O gain, establishing gradient descent’s first accelerated convergence rate in this setting. Namely, we … Read more
\(\) We introduce a notion of self-concordant smoothing for minimizing the sum of two convex functions, one of which is smooth and the other may be nonsmooth. The key highlight of our approach is in a natural property of the resulting problem’s structure which provides us with a variable-metric selection method and a step-length selection … Read more
We propose the use of a conjecturing machine that suggests feature relationships in the form of bounds involving nonlinear terms for numerical features and boolean expressions for categorical features. The proposed Conjecturing framework recovers known nonlinear and boolean relationships among features from data. In both settings, true underlying relationships are revealed. We then compare the … Read more
This paper is devoted to study the convergence rates of a second-order dynamical system and its corresponding discretization associated with a continuously differentiable bilinearly coupled convex-concave saddle point problem. First, we consider the second-order dynamical system with asymptotically vanishing damping term and show the existence and uniqueness of the trajectories as global twice continuously differentiable … Read more
In this paper, we propose an innovative variable fixing strategy called deep Lagrangian underestimate fixing (DeLuxing). It is a highly effective approach for removing unnecessary variables in column-generation (CG)-based exact methods used to solve challenging discrete optimization problems commonly encountered in various industries, including vehicle routing problems (VRPs). DeLuxing employs a novel linear programming (LP) … Read more