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Optimization and nonsmooth analysis
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TLDR
The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.Abstract:
1. Introduction and Preview 2. Generalized Gradients 3. Differential Inclusions 4. The Calculus of Variations 5. Optimal Control 6. Mathematical Programming 7. Topics in Analysis.read more
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Journal ArticleDOI
Modeling, Analysis, and Optimal Control of a Class of HybridSystems
TL;DR: A modeling framework is proposed for a class of hybrid systems which arise in many manufacturing environments and study related optimal control problems and uses calculus of variations techniques to obtain structural properties and an explicit algorithm for deriving optimal policies.
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Convex Image Denoising via Non-convex Regularization with Parameter Selection
TL;DR: A convex non-convex (CNC) denoising variational model for restoring images corrupted by additive white Gaussian noise and an efficient minimization algorithm based on the alternating direction method of multipliers (ADMM) strategy are proposed, which guarantee convergence to a unique global minimizer.
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Dini derivatives in optimization — Part I
Giorgio Giorgi,S. Komlósi +1 more
TL;DR: In this article, general properties of Dini derivatives of functions of one and several variables are studied and some applications of this topic to the study of generalized convexity and generalized optimality conditions for mathematical programming problems.
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Fuzzy necessary optimality conditions for vector optimization problems
Marius Durea,Christiane Tammer +1 more
TL;DR: Lagrange multiplier rules for vector optimization problems are derived using a non-convex separation technique and the concept of abstract subdifferential using a method of estimation of the norms of such multipliers in very general cases and for many particular subdifferentials.
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Extension of Subgradient Techniques for Nonsmooth Optimization in Banach Spaces
Ya. I. Alber,Alfredo N. Iusem +1 more
TL;DR: In this article, the subgradient method for nonsmooth convex constrained minimization problems in a uniformly convex and uniformly smooth Banach space was studied and the case when the stepsizes satisfy ∑k=1∞αk=∞, lim k→∞ αk=0.