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CONSTRAINED FRACTIONAL OPTIMIZATION PROBLEMS AND CORRESPONDING SADDLE-POINT OPTIMALITY CRITERIA

Part of: Optimality conditions Real functions

Published online by Cambridge University Press:  23 October 2025

OCTAVIAN POSTAVARU ,
ANTONELA TOMA  and
SAVIN TREANŢĂ Open the ORCID record for SAVIN TREANŢĂ [Opens in a new window]
OCTAVIAN POSTAVARU
Affiliation:
Center for Research and Training in Innovative Techniques of Applied Mathematics in Engineering, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania; e-mail: opostavaru@linuxmail.org, antonela2222@yahoo.com
ANTONELA TOMA
Affiliation:
Center for Research and Training in Innovative Techniques of Applied Mathematics in Engineering, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania; e-mail: opostavaru@linuxmail.org, antonela2222@yahoo.com
SAVIN TREANŢĂ*
Affiliation:
Department of Applied Mathematics, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania Fundamental Sciences Applied in Engineering – Research Center (SFAI), National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
*
e-mail: savin_treanta@yahoo.com
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Abstract

This research introduces an adapted multidimensional fractional optimal control problem, developed from a newly established framework that combines first-order partial differential equations (PDEs) with inequality constraints. We methodically establish and demonstrate the optimality conditions relevant to this framework. Moreover, we illustrate that, under certain generalized convexity assumptions, there exists a correspondence between the optimal solution of the multidimensional fractional optimal control problem and a saddle point related to the Lagrange functional of the revised formulation. To emphasize the significance and practical implications of our findings, we present several illustrative examples.

Keywords

Riemann–Liouville integralsaddle pointoptimal controlgeneralized convexity

MSC classification

Primary: 49K20: Problems involving partial differential equations
Secondary: 49K35: Minimax problems 26A33: Fractional derivatives and integrals

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 67 , 2025 , e35
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of the Australian Mathematical Publishing Association Inc.

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