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Optimization and nonsmooth analysis
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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
Sensitivity Analysis for Two-Level Value Functions with Applications to Bilevel Programming
TL;DR: It is shown in this research that although the process of deriving necessary optimality conditions for the latter problem is more involved, the conditions themselves do not---to a large extent---differ from those known for the conventional problem.
Journal ArticleDOI
Robust Distributed Linear Programming
Dean Richert,Jorge E. Cortes +1 more
TL;DR: In this paper, a robust, distributed algorithm to solve general linear programs is presented, based on the characterization of the solutions of the linear program as saddle points of a modified Lagrangian function.
Journal ArticleDOI
On finite termination of an iterative method for linear complementarity problems
Andreas Fischer,Christian Kanzow +1 more
TL;DR: A Newton-type method will be described for the solution of LCPs and it will be shown that this method has a finite termination property, i.e., if an iterate is sufficiently close to a solution ofLCP, the method finds this solution in one step.
Journal ArticleDOI
Neural network for solving convex quadratic bilevel programming problems
TL;DR: Using the idea of successive approximation, a neural network to solve convex quadratic bilevel programming problems (CQBPP) is proposed, which is modeled by a nonautonomous differential inclusion and has the least number of state variables and simple structure.
Book ChapterDOI
Perturbation Analysis of Production Networks
TL;DR: This chapter treats the problem of evaluating the sensitivity of performance measures to changes in system parameters for a class of stochastic models, called perturbation analysis, based either on a simulation or on real data.