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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
Optimality conditions for bilevel programming problems
Jane J. Ye,Daoli Zhu +1 more
TL;DR: It is shown that in general the usual constraint qualifications do not hold and the right constraint qualification is the calmness condition, and it is also shown that the linear bilevel programming problem and the minmax problem satisfy the Calmness condition automatically.
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Local Strong Homogeneity of a Regularized Estimator
TL;DR: This paper deals with regularized pointwise estimation of discrete signals which contain large strongly homogeneous zones, where typically they are constant, or linear, or more generally satisfy a linear equation.
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Solution of monotone complementarity problems with locally Lipschitzian functions
TL;DR: IfF is monotone in a neighbourhood ofx, it is proved that 0 εδθ(x) is necessary and sufficient forx to be a solution of CP(F) and the generalized Newton method is shown to be locally well defined and superlinearly convergent with the order of 1+p.
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Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems
Jitka Dupačová,Roger J.-B. Wets +1 more
TL;DR: In this paper, the authors studied the asymptotic behavior of the statistical estimators that maximize a not necessarily dieren tiable criterion function, possibly subject to side constraints (equalities and inequalities).
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A Second-Order Multi-Agent Network for Bound-Constrained Distributed Optimization
Qingshan Liu,Jun Wang +1 more
TL;DR: This technical note presents a second-order multi-agent network for distributed optimization with a sum of convex objective functions subject to bound constraints that is capable of solving more general constrained distributed optimization problems.