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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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A Stochastic Multiple-Leader Stackelberg Model: Analysis, Computation, and Application
Victor DeMiguel,Huifu Xu +1 more
TL;DR: This work studies an oligopoly consisting of M leaders and N followers that supply a homogeneous product (or service) noncooperatively and proposes a computational approach to find the equilibrium based on the sample average approximation method and analyze its rate of convergence.
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Exact Penalization and Necessary Optimality Conditions for Generalized Bilevel Programming Problems
Jane J. Ye,Daoli Zhu,Qiji J. Zhu +2 more
TL;DR: This paper proves that if the objective function of a GBLP is uniformly Lipschitz continuous in the lower level decision variable with respect to the upper level decisionVariable, then using certain uniform parametric error bounds as penalty functions gives single level problems equivalent to the GBLPs.
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Approximate subdifferentials and applications 3: the metric theory
TL;DR: In this paper, a calculus of convex subdifferentials and generalized gradients of Clarke (henceforth sometimes abbreviated C.G.C) is presented, and it is shown that approximate sub-differentials are minimal (as sets) among all possible subdifferential satisfying one or another set of conditions.
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On Fréchet Subdifferentials
TL;DR: A survey of Fréchet subdifferentiation can be found in this article, where the authors discuss fuzzy results in terms of simple subdifferentials calculated at some points arbitrarily close to the point under consideration.
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Nonsmooth optimization through Mesh Adaptive Direct Search and Variable Neighborhood Search
TL;DR: This paper proposes a way to combine the Mesh Adaptive Direct Search (MADS) algorithm, which extends the Generalized Pattern Search algorithm, with the Variable Neighborhood Search (VNS) metaheuristic, for nonsmooth constrained optimization.