We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a composition of a proper closed convex function P and a nonzero affine map, with the … Read more
We investigate constrained first order techniques for training Support Vector Machines (SVM) for online classification tasks. The methods exploit the structure of the SVM training problem and combine ideas of incremental gradient technique, gradient acceleration and successive simple calculations of Lagrange multipliers. Both primal and dual formulations are studied and compared. Experiments show that the … Read more
We investigate the control of constrained stochastic linear systems when faced with only limited information regarding the disturbance process, i.e. when only the first two moments of the disturbance distribution are known. We consider two types of distributionally robust constraints. The constraints of the first type are required to hold with a given probability for … Read more
We consider a problem of maximization of the distance traveled by a material point in the presence of a nonlinear friction under a bounded thrust and fuel expenditure. Using the maximum principle we obtain the form of optimal control and establish conditions under which it contains a singular subarc. This problem seems to be the … Read more
We propose a dynamic programming algorithm for projection onto wavelet tree structures. In contrast to other recently proposed algorithms which only give approximate tree projections for a given sparsity, our algorithm is guaranteed to calculate the projection exactly. We also prove that our algorithm has O(Nk) complexity, where N is the signal dimension and k … Read more
A new algorithm for the solution of multimaterial topology optimization problems is introduced in the present study. The presented method is based on the splitting of a multiphase topology optimization problem into a series of binary phase topology optimization sub-problems which are solved partially, in a sequential manner, using a traditional binary phase topology optimization … Read more
In this paper, we consider mixed integer linear programming (MIP) formulations for piecewise linear functions (PLFs) that are evaluated when an indicator variable is turned on. We describe modifications to standard MIP formulations for PLFs with desirable theoretical properties and superior computational performance in this context. CitationTechnical Report #1788, Computer Sciences Department, University of Wisconsin-Madison.ArticleDownload … Read more
Recent studies in theoretical computer science have exploited new algorithms and methodologies based on statistical physics for investigating the structure and the properties of the Satisfiability problem. We propose a characterization of the SAT problem as a physical system, using both quantum and classical statistical-physical models. We associate a graph to a SAT instance and … Read more
The Rayleigh-Ritz (RR) procedure, including orthogonalization, constitutes a major bottleneck in computing relatively high dimensional eigenspaces of large sparse matrices. Although operations involved in RR steps can be parallelized to a certain level, their parallel scalability, which is limited by some inherent sequential steps, is lower than dense matrix-matrix multiplications. The primary motivation of this … Read more
Power grid vulnerability is a major concern of modern society, and its protection problem is often formulated as a tri-level defender-attacker-defender model. However, this tri-level problem is compu- tationally challenging. In this paper, we design and implement a Column-and-Constraint Generation algorithm to derive its optimal solutions. Numerical results on an IEEE system show that: (i) … Read more