Results 21 to 30 of about 508 (181)
Axioms, 2022 In this paper, we introduce a second-order strong subdifferential of set-valued maps, and discuss some properties, such as convexity, sum rule and so on.
Yuwen Zhai, Qilin Wang, Tian Tang
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Directed Subdifferentiable Functions and the Directed Subdifferential Without Delta-Convex Structure [PDF]
Journal of Optimization Theory and Applications, 2013 We show that the directed subdifferential introduced for differences of convex (delta-convex, DC) functions by Baier and Farkhi can be constructed from the directional derivative without using any information on the DC structure of the function.
Robert Baier +2 more
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AxiomsClarke subdifferential and directional derivative theories are well developed for real functions. However, the nonsmooth analysis framework for interval mappings is still incomplete.
Shexiang Hai, Yanmei Zhang
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Journal of Agricultural Economics, EarlyView.ABSTRACT We develop a framework for regulated production systems where output generation and pollution abatement impose competing technological demands. Using a multi‐ware technology, we model the production set as the intersection of two input requirement frontiers, one for production and one for abatement, each reflecting distinct trade‐offs.
Youpei Yan, Robert G. Chambers
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Journal of Mathematical Sciences, 2003 The author gives a survey (with over 100 references) about the theory of Fréchet subdifferentiation in Banach spaces. After the definitions of Fréchet subdifferentials (and superdifferentials) of real-valued functions, Fréchet normal cones of sets and Fréchet coderivatives of set-valued mappings, the most important properties of these notions are ...
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Sparse Minimum Redundancy Maximum Relevance for Feature Selection
Scandinavian Journal of Statistics, EarlyView.ABSTRACT We propose a feature screening method that integrates both feature–feature and feature–target relationships. Inactive features are identified via a penalized minimum Redundancy Maximum Relevance (mRMR) procedure, which is the continuous version of the classical mRMR penalized by a non‐convex regularizer, and where the parameters estimated as ...
Peter Naylor +3 more
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Efficient Automatic Subdifferentiation for Programs with Linear Branches
Mathematics, 2023 Computing an element of the Clarke subdifferential of a function represented by a program is an important problem in modern non-smooth optimization.
Sejun Park
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International Journal for Numerical Methods in Engineering, Volume 127, Issue 12, 30 June 2026.ABSTRACT Limit analysis and yield design provide a well‐defined mathematical framework for upscaling the strength properties of heterogeneous materials. These techniques can be incorporated into an FFT‐based computational micromechanics framework to evaluate the strength of heterogeneous materials, based on images of their microstructure.
Elodie Donval, Matti Schneider
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Sufficient Optimality and Sensitivity Analysis of a Parameterized Min-Max Programming
Journal of Applied Mathematics, 2012 Sufficient optimality and sensitivity of a parameterized min-max programming with fixed feasible set are analyzed. Based on Clarke's subdifferential and Chaney's second-order directional derivative, sufficient optimality of the parameterized min-max ...
Huijuan Xiong, Yu Xiao, Chaohong Song
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On Cahn–Hilliard Type Viscoelastoplastic Two‐Phase Flows
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.ABSTRACT This contribution deals with a model for viscoelastoplastic two‐phase flows of Cahn–Hilliard type. We present the modeling framework for the flow, the notion of a generalized solution, namely the so‐called dissipative solution, and the key ideas of the existence proof.
Fan Cheng +2 more
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