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作者：Kouri, Drew P.
作者单位：United States Department of Energy (DOE); Sandia National Laboratories
摘要：We develop a general risk quadrangle that gives rise to a large class of spectral risk measures. The statistic of this new risk quadrangle is the average value-at-risk at a specific confidence level. As such, this risk quadrangle generates a continuum of error measures that can be used for superquantile regression. For risk-averse optimization, we introduce an optimal approximation of spectral risk measures using quadrature. We prove the consistency of this approximation and demonstrate our re...
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作者：Lamm, Michael; Lu, Shu
作者单位：SAS Institute Inc; University of North Carolina; University of North Carolina Chapel Hill
摘要：Stochastic variational inequalities (SVI) provide a unified framework for the study of a general class of nonlinear optimization and Nash-type equilibrium problems with uncertain model data. Often the true solution to an SVI cannot be found directly and must be approximated. This paper considers the use of a sample average approximation (SAA), and proposes a new method to compute confidence intervals for individual components of the true SVI solution based on the asymptotic distribution of SAA...
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作者：Nouiehed, Maher; Pang, Jong-Shi; Razaviyayn, Meisam
作者单位：University of Southern California
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作者：Aouad, Ali; Segev, Danny
作者单位：University of London; London Business School; University of Haifa
摘要：In the last two decades, a steady stream of research has been devoted to studying various computational aspects of the ordered k-median problem, which subsumes traditional facility location problems (such as median, center, p-centrum, etc.) through a unified modeling approach. Given a finite metric space, the objective is to locate k facilities in order to minimize the ordered median cost function. In its general form, this function penalizes the coverage distance of each vertex by a multiplic...
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作者：Curtis, Frank E.; Robinson, Daniel P.
作者单位：Lehigh University; Johns Hopkins University
摘要：This paper addresses the question of whether it can be beneficial for an optimization algorithm to follow directions of negative curvature. Although prior work has established convergence results for algorithms that integrate both descent and negative curvature steps, there has not yet been extensive numerical evidence showing that such methods offer consistent performance improvements. In this paper, we present new frameworks for combining descent and negative curvature directions: alternatin...
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作者：Eisenach, Carson; Liu, Han
作者单位：Princeton University; Northwestern University
摘要：Motivated by the task of clustering either d variables or d points into K groups, we investigate efficient algorithms to solve the Peng-Wei (P-W) K-means semi-definite programming (SDP) relaxation. The P-W SDP has been shown in the literature to have good statistical properties in a variety of settings, but remains intractable to solve in practice. To this end we propose FORCE, a new algorithm to solve this SDP relaxation. Compared to off-the-shelf interior point solvers, our method reduces th...
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作者：Ho, Michael; Xin, Jack
作者单位：University of California System; University of California Irvine
摘要：Estimation of the covariance matrix of asset returns from high frequency data is complicated by asynchronous returns, market microstructure noise and jumps. One technique for addressing both asynchronous returns and market microstructure is the Kalman-Expectation-Maximization (KEM) algorithm. However the KEM approach assumes log-normal prices and does not address jumps in the return process which can corrupt estimation of the covariance matrix. In this paper we extend the KEM algorithm to pric...
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作者：Banert, Sebastian; Bot, Radu Ioan
作者单位：Royal Institute of Technology; University of Vienna
摘要：The possibilities of exploiting the special structure of d.c. programs, which consist of optimising the difference of convex functions, are currently more or less limited to variants of the DCA proposed by Pham Dinh Tao and Le Thi Hoai An in 1997. These assume that either the convex or the concave part, or both, are evaluated by one of their subgradients. In this paper we propose an algorithm which allows the evaluation of both the concave and the convex part by their proximal points. Addition...
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作者：Sun, Tianxiao; Quoc Tran-Dinh
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We study the smooth structure of convex functions by generalizing a powerful concept so-called self-concordance introduced by Nesterov and Nemirovskii in the early 1990s to a broader class of convex functions which we call generalized self-concordant functions. This notion allows us to develop a unified framework for designing Newton-type methods to solve convex optimization problems. The proposed theory provides a mathematical tool to analyze both local and global convergence of Newton-type m...
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作者：Hajinezhad, Davood; Hong, Mingyi
作者单位：SAS Institute Inc; University of Minnesota System; University of Minnesota Twin Cities
摘要：In this paper, we propose a perturbed proximal primal-dual algorithm (PProx-PDA) for an important class of linearly constrained optimization problems, whose objective is the sum of smooth (possibly nonconvex) and convex (possibly nonsmooth) functions. This family of problems can be used to model many statistical and engineering applications, such as high-dimensional subspace estimation and the distributed machine learning. The proposed method is of the Uzawa type, in which a primal gradient de...
