Minimization of Nonconvex Locally Lipschitz Functions Using Mollifier Subdifferentials and Uniform Approximations of Generalized Second Order Derivative, Ph.D. Dissertation Sharif University of Technology ; Mahdavi Amiri, Nezameddin (Supervisor)
Abstract
Here, we first ivestigate some available nonsmooth algorithms indentilying their drawbacks, and then provide some guidelines to avert these drawbacks. We divide the algorithms to two main classes, first order and second order. The main drawback of the second order class of algorithm is that there does not exist any suitable method to approximate the generalized second order derivative. To solve this problem, we construct a uniform approximation for the generalized Hessian matrix of an SC1 function. Using the discrete gradient and the extended second order derivative, we define the discrete Hessian matrix. We construct a sequence of sets, where each set is composed of discrete Hessian...
Cataloging briefMinimization of Nonconvex Locally Lipschitz Functions Using Mollifier Subdifferentials and Uniform Approximations of Generalized Second Order Derivative, Ph.D. Dissertation Sharif University of Technology ; Mahdavi Amiri, Nezameddin (Supervisor)
Abstract
Here, we first ivestigate some available nonsmooth algorithms indentilying their drawbacks, and then provide some guidelines to avert these drawbacks. We divide the algorithms to two main classes, first order and second order. The main drawback of the second order class of algorithm is that there does not exist any suitable method to approximate the generalized second order derivative. To solve this problem, we construct a uniform approximation for the generalized Hessian matrix of an SC1 function. Using the discrete gradient and the extended second order derivative, we define the discrete Hessian matrix. We construct a sequence of sets, where each set is composed of discrete Hessian...
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