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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
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Convergence analysis of the direct algorithm
D. E. Finkel,Carl Tim Kelley +1 more
TL;DR: A subsequential convergence result is proved for the DIRECT algorithm that quantifies some of the convergence observations in the literature and applies to several variations on the original method, including one that will handle general constraints.
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On various notions of regularity of sets in nonsmooth analysis
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Tracking Control for Hybrid Systems With State-Triggered Jumps
TL;DR: A novel definition of the tracking error is proposed that overcomes this problem and Lyapunov-based conditions for the global asymptotic stability of the hybrid reference trajectory are formulated.
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On Second-Order Subdifferentials and Their Applications
TL;DR: Applications of the obtained results to Lipschitzian stability of parametric variational and hemivariational inequalities and efficiently express the derived conditions in terms of the initial data for selected problems of continuum mechanics are provided.
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An LP-Newton method: nonsmooth equations, KKT systems, and nonisolated solutions
TL;DR: The new algorithm improves on known methods and, when particularized to KKT systems derived from optimality conditions for constrained optimization or variational inequalities, it has theoretical advantages even over methods specifically designed to solve such systems.