A Redistributed Proximal Bundle Method for Nonconvex Optimization

Hare, Warren; Sagastizábal, Claudia

doi:10.1137/090754595

Cited by 101 publications

(109 citation statements)

References 23 publications

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“…Not long after works on bundle methods for the convex case were first developed, the problem of (locally) minimizing a nonsmooth nonconvex function using exact information was considered in [20,36] and more recently in [1,18,23,31,37]. Many of these bundle methods were developed from a "dual" point of view.…”

Section: Example 3 (Stochastic Simulations)mentioning

confidence: 99%

“…That is, they focus on driving certain convex combinations of subgradients towards satisfaction of first order optimality conditions [27,28,30,[34][35][36]. Except for [18], all of these methods handle nonconvexity by downshitfing the so-called linearization errors if they are negative. The method of [18] tilts the slopes in addition to downshifting.…”

Section: Example 3 (Stochastic Simulations)mentioning

confidence: 99%

“…Except for [18], all of these methods handle nonconvexity by downshitfing the so-called linearization errors if they are negative. The method of [18] tilts the slopes in addition to downshifting. Our algorithm here is along the lines of [18].…”

Section: Example 3 (Stochastic Simulations)mentioning

confidence: 99%

“…The method of [18] tilts the slopes in addition to downshifting. Our algorithm here is along the lines of [18].…”

Section: Example 3 (Stochastic Simulations)mentioning

confidence: 99%

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A proximal bundle method for nonsmooth nonconvex functions with inexact information

2015

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For a class of nonconvex nonsmooth functions, we consider the problem of computing an approximate critical point, in the case when only inexact information about the function and subgradient values is available. We assume that the errors in function and subgradient evaluations are merely bounded, and in principle need not vanish in the limit. We examine the redistributed proximal bundle approach in this setting, and show that reasonable convergence properties are obtained. We further consider a battery of difficult nonsmooth nonconvex problems, made even more difficult by introducing inexactness in the available information. We verify that very satisfactory outcomes are obtained in our computational implementation of the inexact algorithm.

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Section: Example 3 (Stochastic Simulations)mentioning

confidence: 99%

Section: Example 3 (Stochastic Simulations)mentioning

confidence: 99%

Section: Example 3 (Stochastic Simulations)mentioning

confidence: 99%

“…The method of [18] tilts the slopes in addition to downshifting. Our algorithm here is along the lines of [18].…”

Section: Example 3 (Stochastic Simulations)mentioning

confidence: 99%

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A proximal bundle method for nonsmooth nonconvex functions with inexact information

2015

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“…This feature is particularly important for nonconvex bundle methods, which need to handle very carefully cutting-planes models (in some cases a tangent line of a nonconvex function can cut-off a section of the graph of the function, leaving out a critical point, for example), [HS10].…”

Section: Outer Function and Conceptual Modelmentioning

confidence: 99%

Composite proximal bundle method

Sagastizábal

2012

Math. Program.

Self Cite

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We consider minimization of nonsmooth functions which can be represented as the composition of a positively homogeneous convex function and a smooth mapping. This is a sufficiently rich class that includes max-functions, largest eigenvalue functions, and norm-1 regularized functions. The bundle method uses an oracle that is able to compute separately the function and subgradient information for the convex function, and the function and derivatives for the smooth mapping. With this information, it is possible to solve approximately certain proximal linearized subproblems in which the smooth mapping is replaced by its Taylor-series linearization around the current serious step. Our numerical results show the good performance of the Composite Bundle method for a large class of problems.

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Exact penalty functions for optimal control problems I: Main theorem and free‐endpoint problems

Долгополик

Fominyh

2019

Optim Control Appl Methods

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Summary In this two‐part study, we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal and state constraints, problems involving differential inclusions, and optimal control problems for linear evolution equations. This approach allows one to simplify an optimal control problem by removing some (or all) constraints of this problem with the use of an exact penalty function, thus allowing one to reduce optimal control problems to equivalent variational problems and apply numerical methods for solving, eg, problems without state constraints, to problems including such constraints, etc. In the first part of our study, we strengthen some existing results on exact penalty functions for optimisation problems in infinite dimensional spaces and utilise them to study exact penalty functions for free‐endpoint optimal control problems, which reduce these problems to equivalent variational ones. We also prove several auxiliary results on integral functionals and Nemytskii operators that are helpful for verifying the assumptions under which the proposed penalty functions are exact.

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A Redistributed Proximal Bundle Method for Nonconvex Optimization

Cited by 101 publications

References 23 publications

A proximal bundle method for nonsmooth nonconvex functions with inexact information

A proximal bundle method for nonsmooth nonconvex functions with inexact information

Composite proximal bundle method

Exact penalty functions for optimal control problems I: Main theorem and free‐endpoint problems

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