Open AccessBook
Optimization and nonsmooth analysis
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
Citations
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Journal ArticleDOI
A linesearch-based derivative-free approach for nonsmooth constrained optimization ∗
TL;DR: This paper proposes new linesearch-based methods for nonsmooth constrained optimization problems when first-order information on the problem functions is not available and uses the framework developed for the bound-constrained case to solve the penalized problem.
Journal ArticleDOI
Well-posedness of Hemivariational Inequalities and Inclusion Problems
TL;DR: In this article, the authors generalize the concept of well-posedness to a hemivariational inequality and derive some conditions under which the inequality is strongly wellposed in the generalized sense.
Journal ArticleDOI
On nondifferentiable and nonconvex vector optimization problems
Qamrul Hasan Ansari,Jen-Chih Yao +1 more
TL;DR: In this article, the equivalence among the Minty vector variational-like inequality, the Stampacchia variational like inequality, and a non-convex vector optimization problem is established.
Journal ArticleDOI
On Affine-Scaling Interior-Point Newton Methods for Nonlinear Minimization with Bound Constraints
Christian Kanzow,Andreas Klug +1 more
TL;DR: A class of new affine-scaling interior-point Newton-type methods are considered for the solution of optimization problems with bound constraints and are shown to be locally quadratically convergent under the strong second order sufficiency condition without assuming strict complementarity of the solution.
Book ChapterDOI
Nonconvex Superpotentials and Hemivariational Inequalities. Quasidifferentiability in Mechanics
TL;DR: In this paper, the authors studied the question of existence and approximation of the solution of a variationalhemivariational inequality resulting in the delamination theory of von Karman laminated plates.