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作者：Phan, Duy Nhat; Thi, Hoai An Le
作者单位：University System of Ohio; University of Dayton; Universite de Lorraine; Institut Universitaire de France
摘要：In this paper, we focus on the problem of minimizing the sum of a nonconvex differentiable function and a difference of convex (DC) function, where the differentiable function is not restricted to the global Lipschitz gradient continuity assumption. This problem covers a broad range of applications in machine learning and statistics, such as compressed sensing, signal recovery, sparse dictionary learning, matrix factorization, etc. We first take inspiration from the Nesterov acceleration techn...
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作者：Guan, Jiewen; He, Simai; Jiang, Bo; Li, Zhening
作者单位：Shanghai University of Finance & Economics; Shanghai Jiao Tong University; Shanghai University of Finance & Economics; Shanghai University of Finance & Economics; University of Portsmouth
摘要：The spectral p-norm and nuclear p-norm of matrices and tensors appear in various applications, albeit both are NP-hard to compute. The former sets a foundation of & ell; p-sphere-constrained polynomial optimization problems, and the latter has been found in many rank minimization problems in machine learning. We study approximation algorithms of the tensor nuclear p-norm with an aim to establish the approximation bound matching the best one of its dual norm, the tensor spectral p-norm. Driven ...
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作者：Lamperski, Jourdain; Freund, Robert M.; Todd, Michael J.
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; Massachusetts Institute of Technology (MIT); Cornell University
摘要：The ellipsoid algorithm is a fundamental algorithm for computing a solution to the system of m linear inequalities in n variables (P) : A(T)x <= u when its set of solutions has positive volume. However, when (P) is infeasible, the ellipsoid algorithm has no mechanism for proving that (P) is infeasible. This is in contrast to the other two fundamental algorithms for tackling (P), namely, the simplex and interior-point methods, each of which can be easily implemented in a way that either produce...
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作者：Chen, Xi; Ma, Will; Simchi-Levi, David; Xin, Linwei
作者单位：New York University; Columbia University; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University of Chicago
摘要：In this paper, we consider a personalized assortment planning problem under inventory constraints, where each arriving customer type is defined by a primary item of interest. As long as that item is in stock, the customer adds it to the shopping cart, at which point the retailer can recommend to the customer an assortment of add-ons to go along with the primary item. This problem is motivated by the new recommendation at checkout systems that have been deployed at many online retailers, and it...
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作者：Nagarajan, Viswanath; Wang, Lily
作者单位：University of Michigan System; University of Michigan
摘要：We consider a general online network design problem in which a sequence of N requests arrive over time, each of which needs to use some subset of the available resources resource. The objective is to minimize the total cost P E. The cost incurred by a resource e E E is some function fe of the total load le on that eEE fe(le). We focus on cost functions that exhibit (dis)economies of scale. These functions are of the form fe(x) = sigma e + xi e center dot x alpha e if x > 0 (and zero if x = 0),...
