On Lifting Operators and Regularity of Nonsmooth Newton Methods for Optimal Control Problems of Differential Algebraic Equations

Jinhai Chen; Herschel Rabitz

doi:10.1007/s10957-018-1364-8

On Lifting Operators and Regularity of Nonsmooth Newton Methods for Optimal Control Problems of Differential Algebraic Equations

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Abstract

This paper focuses on nonsmooth Newton methods of optimal control problems governed by mixed control–state constraints with differential algebraic equations. In contrast to previous results, we analyze lifting operators involved in nonsmooth Newton methods and establish corresponding convergence results. We also give sufficient conditions for regularity of generalized derivatives of systems of nonsmooth operator equations associated with optimal control problems.

Original language	English (US)
Pages (from-to)	518-535
Number of pages	18
Journal	Journal of Optimization Theory and Applications
Volume	180
Issue number	2
DOIs	https://doi.org/10.1007/s10957-018-1364-8
State	Published - Feb 15 2019

All Science Journal Classification (ASJC) codes

Management Science and Operations Research
Control and Optimization
Applied Mathematics

Keywords

Convergence
Lifting operators
Nonsmooth Newton methods
Optimal control of DAEs
Regularity conditions

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10.1007/s10957-018-1364-8

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abstract = "This paper focuses on nonsmooth Newton methods of optimal control problems governed by mixed control–state constraints with differential algebraic equations. In contrast to previous results, we analyze lifting operators involved in nonsmooth Newton methods and establish corresponding convergence results. We also give sufficient conditions for regularity of generalized derivatives of systems of nonsmooth operator equations associated with optimal control problems.",

keywords = "Convergence, Lifting operators, Nonsmooth Newton methods, Optimal control of DAEs, Regularity conditions",

author = "Jinhai Chen and Herschel Rabitz",

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AU - Rabitz, Herschel

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AB - This paper focuses on nonsmooth Newton methods of optimal control problems governed by mixed control–state constraints with differential algebraic equations. In contrast to previous results, we analyze lifting operators involved in nonsmooth Newton methods and establish corresponding convergence results. We also give sufficient conditions for regularity of generalized derivatives of systems of nonsmooth operator equations associated with optimal control problems.

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KW - Lifting operators

KW - Nonsmooth Newton methods

KW - Optimal control of DAEs

KW - Regularity conditions

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ER -

On Lifting Operators and Regularity of Nonsmooth Newton Methods for Optimal Control Problems of Differential Algebraic Equations

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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