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作者：Attouch, Hedy; Chbani, Zaki; Fadili, Jalal; Riahi, Hassan
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Montpellier; Cadi Ayyad University of Marrakech; Universite de Caen Normandie; Centre National de la Recherche Scientifique (CNRS)
摘要：In a Hilbert space setting, for convex optimization, we analyze the convergence rate of a class of first-order algorithms involving inertial features. They can be interpreted as discrete time versions of inertial dynamics involving both viscous and Hessian-driven dampings. The geometrical damping driven by the Hessian intervenes in the dynamics in the form del(2) f (x(t)).x(t). By treating this term as the time derivative of del f (x(t)), this gives, in discretized form, first-order algorithms...
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作者：Noyan, Nilay; Merakli, Merve; Kucukyavuz, Simge
作者单位：Sabanci University; Northwestern University
摘要：In this study, we consider two classes of multicriteria two-stage stochastic programs in finite probability spaces with multivariate risk constraints. The first-stage problem features multivariate stochastic benchmarking constraints based on a vector-valued random variable representing multiple and possibly conflicting stochastic performance measures associated with the second-stage decisions. In particular, the aim is to ensure that the decision-based random outcome vector of interest is pref...
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作者：Doikov, Nikita; Nesterov, Yurii
摘要：In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth component, having Lipschitz-continuous high-order derivative. The convergence both in function value and in the norm of minimal subgradient is established. Global complexity bounds for the Composite Tensor Method in convex and uniformly convex cases are also disc...
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作者：Hoa, Le Tuan
作者单位：Vietnam Academy of Science & Technology (VAST)
摘要：The paper provides a connection between Commutative Algebra and Integer Programming and contains two parts. The first one is devoted to the asymptotic behavior of integer programs with a fixed cost linear functional and the constraint sets consisting of a finite system of linear equations or inequalities with integer coefficients depending linearly on n. An integer N-* is determined such that the optima of these integer programs are a quasi-linear function of n for all n >= N-*. Using results ...
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作者：Fan, Jingnan; Ruszczynski, Andrzej
作者单位：Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick
摘要：For controlled discrete-time stochastic processes we introduce a new class of dynamic risk measures, which we call process-based. Their main feature is that they measure risk of processes that are functions of the history of a base process. We introduce a new concept of conditional stochastic time consistency and we derive the structure of process-based risk measures enjoying this property. We show that they can be equivalently represented by a collection of static law-invariant risk measures ...
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作者：Banholzer, Dirk; Fliege, Jorg; Werner, Ralf
作者单位：University of Southampton; University of Augsburg
摘要：We study the rates at which optimal estimators in the sample average approximation approach converge to their deterministic counterparts in the almost sure sense and in mean. To be able to quantify these rates, we consider the law of the iterated logarithm in a Banach space setting and first establish under relatively mild assumptions almost sure convergence rates for the approximating objective functions, which can then be transferred to the estimators for optimal values and solutions of the ...
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作者：Rontsis, Nikitas; Goulart, Paul J.; Nakatsukasa, Yuji
作者单位：University of Oxford; University of Oxford; Research Organization of Information & Systems (ROIS); National Institute of Informatics (NII) - Japan
摘要：We present an algorithm for the minimization of a nonconvex quadratic function subject to linear inequality constraints and a two-sided bound on the 2-norm of its solution. The algorithm minimizes the objective using an active-set method by solving a series of trust-region subproblems (TRS). Underpinning the efficiency of this approach is that the global solution of the TRS has been widely studied in the literature, resulting in remarkably efficient algorithms and software. We extend these res...
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作者：Sur, Arnab; Birge, John R.
作者单位：University of Chicago
摘要：In this article we study the consistency of optimal and stationary (KKT) points of a stochastic non-linear optimization problem involving expectation functionals, when the underlying probability distribution associated with the random variable is weakly approximated by a sequence of random probability measures. The optimization model includes constraints with expectation functionals those are not captured in direct application of the previous results on optimality conditions exist in the liter...
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作者：Rujeerapaiboon, Napat; Schindler, Kilian; Kuhn, Daniel; Wiesemann, Wolfram
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Imperial College London
摘要：The goal of scenario reduction is to approximate a given discrete distribution with another discrete distribution that has fewer atoms. We distinguish continuous scenario reduction, where the new atoms may be chosen freely, and discrete scenario reduction, where the new atoms must be chosen from among the existing ones. Using the Wasserstein distance as measure of proximity between distributions, we identify those n-point distributions on the unit ball that are least susceptible to scenario re...
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作者：Salzo, Saverio; Villa, Silvia
作者单位：Istituto Italiano di Tecnologia - IIT; University of Genoa
摘要：We study the block-coordinate forward-backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to fully exploit the smoothness properties of the objective function. In the convex case and in an infinite dimensional setting, we establish almost sure weak convergence of the iterates and the asymptotic rate o(1/n) for the mean of the function values. We de...
