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作者：Gowda, M. Seetharama; Sossa, David
作者单位：University System of Maryland; University of Maryland Baltimore County; Universidad de O'Higgins
摘要：Given a closed convex cone C in a finite dimensional real Hilbert space H, a weakly homogeneous map fC -> H is a sum of two continuous maps h and g, where h is positively homogeneous of degree gamma (>= 0) on C and g(x)=o(||x||gamma) as ||x||->infinity in C. Given such a map f, a nonempty closed convex subset K of C, and a q is an element of H, we consider the variational inequality problem, VI(f,K,q), of finding an x is an element of K such that f(x)+q,x-x >= 0 for all x is an element of K. I...
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作者：Royset, Johannes O.; Wets, Roger J-B
作者单位：United States Department of Defense; United States Navy; Naval Postgraduate School; University of California System; University of California Davis
摘要：Much of the development of lopsided convergence for bifunctions defined on product spaces was in response to motivating applications. A wider class of applications requires an extension that would allow for arbitrary domains, not only product spaces. This leads to an extension of the definition and its implications that include the convergence of solutions and optimal values of a broad class of minsup problems. In the process we relax the definition of lopsided convergence even for the classic...
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作者：Hantoute, Abderrahim; Henrion, Rene; Perez-Aros, Pedro
作者单位：Universidad de Chile; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth. This fact motivates the consideration of subdifferentials for such typically just continuous functions. The aim of this paper is to provide subdifferential formulae of such functions in the case of Gaussian distributions for possibly infinite-dimensional decision variables and nonsmooth (locally Lipschitzian) input data. These formulae are based on the sphe...
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作者：Berczi, Kristof; Chandrasekaran, Karthekeyan; Kiraly, Tamas; Lee, Euiwoong; Xu, Chao
作者单位：Eotvos Lorand University; University of Illinois System; University of Illinois Urbana-Champaign; Carnegie Mellon University
摘要：In the fixed-terminal bicut problem, the input is a directed graph with two specified nodes s and t and the goal is to find a smallest subset of edges whose removal ensures that s cannot reach tandt cannot reach s. In the global bicut problem, the input is a directed graph and the goal is to find a smallest subset of edges whose removal ensures that there exist two nodes s and t such that s cannot reach tandt cannot reach s. Fixed-terminal bicut and global bicut are natural extensions of {s,t}...
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作者：Huang, Chien-Chung; Kakimura, Naonori; Kamiyama, Naoyuki
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Keio University; Kyushu University
摘要：In this paper, we propose new exact and approximation algorithms for the weighted matroid intersection problem. Our exact algorithm is faster than previous algorithms when the largest weight is relatively small. Our approximation algorithm delivers a (1-E)-approximate solution with a running time significantly faster than most known exact algorithms. The core of our algorithms is a decomposition technique: we decompose an instance of the weighted matroid intersection problem into a set of inst...
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作者：Drusvyatskiy, D.; Paquette, C.
作者单位：University of Washington; University of Washington Seattle
摘要：We consider global efficiency of algorithms for minimizing a sum of a convex function and a composition of a Lipschitz convex function with a smooth map. The basic algorithm we rely on is the prox-linear method, which in each iteration solves a regularized subproblem formed by linearizing the smooth map. When the subproblems are solved exactly, the method has efficiency O(epsilon(-2)), akin to gradient descent for smooth minimization. We show that when the subproblems can only be solved by fir...
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作者：Fujishige, Satoru; Sano, Yoshio; Zhan, Ping
作者单位：Kyoto University; University of Tsukuba
摘要：We present a non-pricing allocation scheme of divisible goods to agents with utility functions and submodular constraints on goods. The main contribution of the present paper is that through our non-pricing allocation scheme we reveal the close relation between (1) the recent results in the allocation schemes of the random assignment problem and its extensions with ordinal or lexicographic preferences on goods and (2) the monotone algorithms of fair (egalitarian) allocations with separable uti...
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作者：Dong, Hongbo; Ahn, Miju; Pang, Jong-Shi
作者单位：Washington State University; University of Southern California
摘要：We introduce a new constraint system for sparse variable selection in statistical learning. Such a system arises when there are logical conditions on the sparsity of certain unknown model parameters that need to be incorporated into their selection process. Formally, extending a cardinality constraint, an affine sparsity constraint (ASC) is defined by a linear inequality with two sets of variables: one set of continuous variables and the other set represented by their nonzero patterns. This pa...
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作者：Qian, Chengde; Quoc Tran-Dinh; Fu, Sheng; Zou, Changliang; Liu, Yufeng
作者单位：Nankai University; University of North Carolina; University of North Carolina Chapel Hill; National University of Singapore; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill
摘要：We consider the classification problem when the input features are represented as matrices rather than vectors. To preserve the intrinsic structures for classification, a successful method is the support matrix machine (SMM) in Luo et al. (in: Proceedings of the 32nd international conference on machine learning, Lille, France, no 1, pp 938-947, 2015), which optimizes an objective function with a hinge loss plus a so-called spectral elastic net penalty. However, the issues of extending SMM to m...
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作者：Eberhard, A. C.; Luo, Y.; Liu, S.
作者单位：Royal Melbourne Institute of Technology (RMIT)
摘要：Under the assumption of prox-regularity and the presence of a tilt stable local minimum we are able to show that a VU like decomposition gives rise to the existence of a smooth manifold on which the function in question coincides locally with a smooth function.
