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Epi-Convergent Discretizations of Multistage Stochastic Programs [PDF]
Mathematics of Operations Research, 2005 In many dynamic stochastic optimization problems in practice, the uncertain factors are best modeled as random variables with an infinite support. This results in infinite-dimensional optimization problems that can rarely be solved directly. Therefore, the random variables (stochastic processes) are often approximated by finitely supported ones ...
Teemu Pennanen
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Epi-convergent Smoothing with Applications to Convex Composite Functions [PDF]
SIAM Journal on Optimization, 2013 Smoothing methods have become part of the standard tool set for the study and solution of nondifferentiable and constrained optimization problems as well as a range of other variational and equilibrium problems. In this note we synthesize and extend recent results due to Beck and Teboulle on infimal convolution smoothing for convex functions with those
James V Burke, Tim Hoheisel
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On the Interchange of Subdifferentiation and Epi-Convergence
Journal of Mathematical Analysis and Applications, 1995 As the title of the paper clearly claimes, conditions are investigated that guarantee the interchange of the subdifferentiation notion and the epi-convergence notion. In particular, the Fréchet subdifferentiation, the limiting subdifferential, and the Clarke subdifferential are considered.
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Epi-convergence of sequences of normal integrands and strong consistency of the maximum likelihood estimator [PDF]
Annals of Statistics, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A characterization of epi-convergence in terms of convergence of level sets [PDF]
Proceedings of the American Mathematical Society, 1992 Let LSC ( X
Beer, Gerald +2 more
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Epi-convergent discretizations of stochastic programs via integration quadratures [PDF]
Numerische Mathematik, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Teemu Pennanen, Matti Koivu
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Epi-Convergence of Expectation Functions under Varying Measures and Integrands
, 2022 For expectation functions on metric spaces, we provide sufficient conditions for epi-convergence under varying probability measures and integrands, and examine applications in the area of sieve estimators, mollifier smoothing, PDE-constrained optimization, and stochastic optimization with expectation constraints.
Feinberg, Eugene A. +2 more
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Epi-convergence: The Moreau Envelope and Generalized Linear-Quadratic Functions [PDF]
Journal of Optimization Theory and Applications, 2018 This work introduces the class of generalized linear-quadratic functions, constructed using maximally monotone symmetric linear relations. Calculus rules and properties of the Moreau envelope for this class of functions are developed. In finite dimensions, on a metric space defined by Moreau envelopes, we consider the epigraphical limit of a sequence ...
Planiden, Chayne, Wang, Xianfu
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Basic properties of statistical epi-convergence
, 2020 Bu çalışmada, istatistiksel epi-yakınsaklığın sonraki çalışmalarda daha verimli kullanılabilmesi için bazı temel özelliklere yer verildi. Bir fonksiyon dizisinin düzgün istatistiksel yakınsaklık durumu, fonksiyon dizilerinin bileşkesinin istatistiksel epi-limiti, fonksiyon dizilerinin toplamının istatistiksel epi-limiti, fonksiyon dizisinin alttan yarı
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Evaluation of the epi-convergence
, 2005 The paper presents an equivalent characterization of the epi-convergence of lower semicontinuous functions. The proposed ‘measures’ naturally estimate the distance between optimal values of two optimization programs. A comparison of optimal solutions is more complex.
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