P-Regularity Theory and Nonlinear Optimization Problems

The paper studies the nonlinear optimization problem in the form of optimal control problem subject to irregular constraints for which the multiplier of the objective function in Pontryagin’s function may vanish. It turns out that in case of p-regularity constraints this drawback can be overcome. Bu...

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Bibliographic Details
Published inOptimization and Applications Vol. 1145; pp. 237 - 253
Main Authors Evtushenko, Yuri, Malkova, Vlasta, Tret’yakov, Alexey
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2020
Springer International Publishing
SeriesCommunications in Computer and Information Science
Subjects
factor operator
Implicit function theorem
Nonlinear boundary value problems
Nonlinear optimization
regularity
Singular optimal control
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ISBN3030386023
9783030386023
ISSN1865-0929
1865-0937
DOI10.1007/978-3-030-38603-0_18

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Summary:The paper studies the nonlinear optimization problem in the form of optimal control problem subject to irregular constraints for which the multiplier of the objective function in Pontryagin’s function may vanish. It turns out that in case of p-regularity constraints this drawback can be overcome. But for this it necessary to prove continuous dependence solution of differential equation with respect to the boundary conditions. We give a new approach to the existence of such solutions via p-regularity theory.
Bibliography:This work was partially supported by the Russian Foundation for Basic Research (project no. 17-07-00510) and by Program 2 of Presidium of RAS “Mechanisms for ensuring fault tolerance in modern high-performance and highly reliable computing”.
ISBN:3030386023
9783030386023
ISSN:1865-0929
1865-0937
DOI:10.1007/978-3-030-38603-0_18