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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 and Duality for Invex Nonsmooth Multiobjective programming problems
Do Sang Kim,Siegfried Schaible +1 more
TL;DR: In this article, the authors consider nonsmooth multiobjective programming problems with inequality and equality constraints involving locally Lipschitz functions and present sufficient optimality conditions under various generalized invexity assumptions and certain regularity conditions.
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A parameterized Newton method and a quasi-Newton method for nonsmooth equations
Xiaojun Chen,Liqun Qi +1 more
TL;DR: This paper presents a parameterized Newton method using generalized Jacobians and a Broyden-like method for solving nonsmooth equations that ensures that the method is well-defined even when the generalized Jacobian is singular.
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Generalized directional gradients, backward stochastic differential equations and mild solutions of semilinear parabolic equations
TL;DR: In this paper, a forward-backward system of stochastic differential equations in an infinite-dimensional framework and its relationship with a semilinear parabolic differential equation on a Hilbert space is studied.
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The SECQ, Linear Regularity, and the Strong CHIP for an Infinite System of Closed Convex Sets in Normed Linear Spaces
TL;DR: A property relating their epigraphs with their intersection's epigraph is studied, and its relations to other constraint qualifications (such as the linear regularity, the strong CHIP, and Jameson's ($G$)-property) are established.
On algorithms for solving least squares problems under an L1 penalty or an L1 constraint
TL;DR: Several algorithms can be used to calculate the LASSO solution by minimising the residual sum of squares subject to a constraint (penalty) on the sum of the absolute values of the coefficient estimates.