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作者：Pang, Jong-Shi; Stewart, David E.
作者单位：Rensselaer Polytechnic Institute; Rensselaer Polytechnic Institute; University of Iowa
摘要：In the first part of this paper, we establish several sensitivity results of the solution x(t, xi) to the ordinary differential equation (ODE) initial-value problem (IVP) dx/dt = f (x), x(0) = xi as a function of the initial value xi for a non differentiable f (x). Specifically, we show that for Xi(T) = {x(t, xi(0)) : 0 <= t <= T}, (a) if f is B-differentiable on Xi(T), then so is the solution operator x (t; .) at xi(0); (b) if f is semismooth on Xi(T), then so is x(t; .) at xi(0); (c) if f ha...
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作者：Deng, Geng; Ferris, Michael C.
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
摘要：The sample-path method is one of the most important tools in simulation-based optimization. The basic idea of the method is to approximate the expected simulation output by the average of sample observations with a common random number sequence. In this paper, we describe a new variant of Powell's unconstrained optimization by quadratic approximation (UOBYQA) method, which integrates a Bayesian variable-number sample-path (VNSP) scheme to choose appropriate number of samples at each iteration....
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作者：Tseng, Paul
作者单位：University of Washington; University of Washington Seattle
摘要：An important issue in convex programming concerns duality gap. Various conditions have been developed over the years that guarantee no duality gap, including one developed by Rockafellar (Network flows and monotropic programming. Wiley-Interscience, New York, 1984)involving separable objective function and affine constraints. We show that this sufficient condition can be further relaxed to allow the constraint functions to be separable. We also refine a sufficient condition involving weakly an...
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作者：Bonnans, J. Frederic; Hermant, Audrey
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：The paper deals with optimal control problems with only one control variable and one state constraint, of arbitrary order. We consider the case of finitely many boundary arcs and touch times. We obtain a no-gap theory of second-order conditions, allowing to characterize second-order quadratic growth.
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作者：Correa, Rafael; Gajardo, Pedro; Thibault, Lionel
作者单位：Universidad Tecnica Federico Santa Maria; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad de Chile; Universite de Montpellier
摘要：We prove in the general setting of lower semicontinuous functions on Banach spaces the relation between the Rockafellar directional derivative and the mixed lower limit of the lower Dini derivatives. As a byproduct we derive the famous inclusions of tangent cones of closed sets in Banach spaces. The results are established using as principal tool multidirectional mean value inequalities [Aussel et al., SIAM J Optim 9(3), 690-706 (1999)].
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作者：Mordukhovich, B. S.; Nam, N. M.; Yen, N. D.
作者单位：Wayne State University; Vietnam Academy of Science & Technology (VAST)
摘要：In this paper we derive new results for computing and estimating the so-called Frechet and limiting (basic and singular) subgradients of marginal functions in real Banach spaces and specify these results for important classes of problems in parametric optimization with smooth and nonsmooth data. Then we employ them to establish new calculus rules of generalized differentiation as well as efficient conditions for Lipschitzian stability and optimality in nonlinear and nondifferentiable programmi...
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作者：Facchinei, Francisco; Fischer, Andreas; Piccialli, Veronica
作者单位：Sapienza University Rome; Technische Universitat Dresden
摘要：The generalized Nash equilibrium problem, where the feasible sets of the players may depend on the other players' strategies, is emerging as an important modeling tool. However, its use is limited by its great analytical complexity. We consider several Newton methods, analyze their features and compare their range of applicability. We illustrate in detail the results obtained by applying them to a model for internet switching.
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作者：Daniilidis, A.; Jules, F.; Lassonde, M.
作者单位：Universite des Antilles; Autonomous University of Barcelona
摘要：It is known that a locally Lipschitz function is approximately convex if, and only if, its Clarke subdifferential is a submonotone operator. The main object of this work is to extend the above characterization to the class of lower semicontinuous functions. To this end, we establish a new approximate mean value inequality involving three points. We also show that an analogue of the Rockafellar maximal monotonicity theorem holds for this class of functions and we discuss the case of arbitrary s...
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作者：Goberna, Miguel A.; Todorov, Maxim I.
作者单位：Universitat d'Alacant; Universidad Americas Puebla (UDLAP)
摘要：Any linear (ordinary or semi-infinite) optimization problem, and also its dual problem, can be classified as either inconsistent or bounded or unbounded, giving rise to nine duality states, three of them being precluded by the weak duality theorem. The remaining six duality states are possible in linear semi-infinite programming whereas two of them are precluded in linear programming as a consequence of the existence theorem and the non-homogeneous Farkas Lemma. This paper characterizes the li...
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作者：Lin, Gui-Hua; Chen, Xiaojun; Fukushima, Masao
作者单位：Kyoto University; Dalian University of Technology; Hirosaki University
摘要：In this paper, we consider the stochastic mathematical programs with linear complementarity constraints, which include two kinds of models called here-and-now and lower-level wait-and-see problems. We present a combined smoothing implicit programming and penalty method for the problems with a finite sample space. Then, we suggest a quasi-Monte Carlo approximation method for solving a problem with continuous random variables. A comprehensive convergence theory is included as well. We further re...
