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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
A Neurodynamic Optimization Approach to Bilevel Quadratic Programming
Sitian Qin,Xinyi Le,Jun Wang +2 more
TL;DR: It is proved that the proposed neural network for bilevel linear programming is convergent to an equilibrium point in finite time and is guaranteed for delivering the exact optimal solutions to any convex BQP problems.
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A configuration space analysis of bodies in contact. I: 1st order mobility
Elon Rimon,Joel W. Burdick +1 more
TL;DR: In this article, a configuration space method for analyzing the relative mobility of a body B, in frictionless quasi-static contact with rigid stationary bodies A 1, A 2, A 3, A 4, A 5, A 6, A 7, A 8, A 9, A 10, A 11, A 12.
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Lyapounov Functions of closed Cone Fields: from Conley Theory to Time Functions.
TL;DR: In this paper, a theory a la Conley is proposed for cone fields using a notion of relaxed orbits based on cone enlargements, in the spirit of space time geometry, which generalizes the equivalence between stable causality and the existence of temporal functions.
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Extremal solutions of quasilinear parabolic inclusions with generalized Clarke's gradient
Siegfried Carl,Dumitru Motreanu +1 more
TL;DR: In this article, the authors considered an initial boundary value problem for a parabolic inclusion whose multivalued nonlinearity is characterized by Clarke's generalized gradient of some locally Lipschitz function, and whose elliptic operator may be a general quasilinear operator of Leray-Lions type.
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Constraint Qualifications and KKT Conditions for Bilevel Programming Problems
TL;DR: This paper extends well-known constraint qualifications for nonlinear programming problems and derives a Karash-Kuhn-Tucker (KKT)-type necessary optimality condition under these constraint qualifications without assuming the lower-level problem satisfying the Mangasarian Fromovitz constraint qualification.