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A class of multiobjective control problems
Author(s) -
de Oliveira V. A.,
Silva G. N.,
RojasMedar M. A.
Publication year - 2008
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.863
Subject(s) - pontryagin's minimum principle , class (philosophy) , optimal control , mathematical optimization , mathematics , maximum principle , scalar (mathematics) , set (abstract data type) , multi objective optimization , computer science , geometry , artificial intelligence , programming language
We introduce the class of MP‐pseudoinvex multiobjective optimal control problems. We show that the concept of MP‐pseudoinvexity is a sufficient condition of optimality and, further, that problems such that every control process satisfying Pontryagin's maximum principle is an optimal process are necessarily MP‐pseudoinvex problems. Moreover, a sub‐class of the MP‐pseudoinvex problems, which we call MP‐invex multiobjective optimal control problems, is defined. We prove that the set of optimal solutions of MP‐invex multiobjective problems coincides with the set of optimal solutions of a related scalar problem. Copyright © 2008 John Wiley & Sons, Ltd.