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作者：Fawzi, Hamza; Parrilo, Pablo A.
作者单位：Massachusetts Institute of Technology (MIT)
摘要：The nonnegative rank of a matrix A is the smallest integer r such that A can be written as the sum of r rank-one nonnegative matrices. The nonnegative rank has received a lot of attention recently due to its application in optimization, probability and communication complexity. In this paper we study a class of atomic rank functions defined on a convex cone which generalize several notions of positive ranks such as nonnegative rank or cp-rank (for completely positive matrices). The main contri...
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作者：Byrd, Richard H.; Nocedal, Jorge; Oztoprak, Figen
作者单位：University of Colorado System; University of Colorado Boulder; Northwestern University; Istanbul Bilgi University
摘要：We study a Newton-like method for the minimization of an objective function that is the sum of a smooth function and an regularization term. This method, which is sometimes referred to in the literature as a proximal Newton method, computes a step by minimizing a piecewise quadratic model of the objective function . In order to make this approach efficient in practice, it is imperative to perform this inner minimization inexactly. In this paper, we give inexactness conditions that guarantee gl...
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作者：Jiang, Ruiwei; Guan, Yongpei; Watson, Jean-Paul
作者单位：University of Michigan System; University of Michigan; State University System of Florida; University of Florida; United States Department of Energy (DOE); Sandia National Laboratories
摘要：As renewable energy penetration rates continue to increase in power systems worldwide, new challenges arise for system operators in both regulated and deregulated electricity markets to solve the security-constrained coal-fired unit commitment problem with intermittent generation (due to renewables) and uncertain load, in order to ensure system reliability and maintain cost effectiveness. In this paper, we study a security-constrained coal-fired stochastic unit commitment model, which we use t...
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作者：Mitra, Sumit; Garcia-Herreros, Pablo; Grossmann, Ignacio E.
作者单位：Carnegie Mellon University
摘要：We describe a cross-decomposition algorithm that combines Benders and scenario-based Lagrangean decomposition for two-stage stochastic programming investment planning problems with complete recourse, where the first-stage variables are mixed-integer and the second-stage variables are continuous. The algorithm is a novel cross-decomposition scheme and fully integrates primal and dual information in terms of primal-dual multi-cuts added to the Benders and the Lagrangean master problems for each ...
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作者：Gotoh, Jun-ya; Uryasev, Stan
作者单位：Chuo University; State University System of Florida; University of Florida
摘要：This paper studies four families of polyhedral norms parametrized by a single parameter. The first two families consist of the CVaR norm (which is equivalent to the D-norm, or the largest- norm) and its dual norm, while the second two families consist of the convex combination of the - and -norms, referred to as the deltoidal norm, and its dual norm. These families contain the - and -norms as special limiting cases. These norms can be represented using linear programming (LP) and the size of L...
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作者：Seeger, Alberto; Torki, Mounir
作者单位：Avignon Universite; Avignon Universite
摘要：We extend John's inscribed ellipsoid theorem, as well as Loewner's circumscribed ellipsoid theorem, from convex bodies to proper cones. To be more precise, we prove that a proper cone in contains a unique ellipsoidal cone of maximal canonical volume and, on the other hand, it is enclosed by a unique ellipsoidal cone of minimal canonical volume. In addition, we explain how to construct the inscribed ellipsoidal cone . The circumscribed ellipsoidal cone is then obtained by duality arguments. The...
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作者：Hanasusanto, Grani A.; Kuhn, Daniel; Wiesemann, Wolfram
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Imperial College London
摘要：Although stochastic programming problems were always believed to be computationally challenging, this perception has only recently received a theoretical justification by the seminal work of Dyer and Stougie (Math Program A 106(3):423-432, 2006). Amongst others, that paper argues that linear two-stage stochastic programs with fixed recourse are #P-hard even if the random problem data is governed by independent uniform distributions. We show that Dyer and Stougie's proof is not correct, and we ...
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作者：Edirisinghe, Chanaka; Jeong, Jaehwan
作者单位：Rensselaer Polytechnic Institute; Radford University
摘要：We present a global algorithm for indefinite knapsack separable quadratic programs with bound constraints. The upper bounds on variables with nonconvex terms are assumed to be infinite in the algorithmic development. By characterizing optimal solutions of the problem, we enumerate a subset of KKT points to determine a global optimum. The enumeration is made efficient by developing a theory for shrinking and partitioning the search domain of KKT multipliers. The global algorithmic procedure is ...
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作者：Neumaier, Arnold
作者单位：University of Vienna
摘要：This paper presents an algorithm for approximately minimizing a convex function in simple, not necessarily bounded convex, finite-dimensional domains, assuming only that function values and subgradients are available. No global information about the objective function is needed apart from a strong convexity parameter (which can be put to zero if only convexity is known). The worst case number of iterations needed to achieve a given accuracy is independent of the dimension and-apart from a cons...
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作者：Gower, R. M.; Gower, A. L.
作者单位：Heriot Watt University; University of Edinburgh; Ollscoil na Gaillimhe-University of Galway
摘要：It is commonly assumed that calculating third order information is too expensive for most applications. But we show that the directional derivative of the Hessian () can be calculated at a cost proportional to that of a state-of-the-art method for calculating the Hessian matrix. We do this by first presenting a simple procedure for designing high order reverse methods and applying it to deduce several methods including a reverse method that calculates . We have implemented this method taking i...
