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Convex and convex-like optimization over a range inclusion problem and first applications

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Listed:
  • Hocine Mokhtar-Kharroubi

    (Université Oran I)

Abstract

The paper deals with the minimization of a function over the solution set of a range inclusion problem determined by a multifunction. A strong Lagrange duality is provided first in terms of a quasirelative interior condition and then under a so-called Assumption (S). When the function and the multifunction are convex, we improve this duality under a closed cone condition. The stability analysis is investigated. In addition, if the multifunction is a convex process, then the Fenchel dual is performed in terms of its conjugate. As a first application, we provide a unified approach to the optimization of general discrete inclusions systems; in particular, we improve several results on optimal control, strong Lagrange duality and Fenchel duality for some classes of convex controlled discrete processes.

Suggested Citation

  • Hocine Mokhtar-Kharroubi, 2017. "Convex and convex-like optimization over a range inclusion problem and first applications," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 277-299, November.
    • Handle: RePEc:spr:decfin:v:40:y:2017:i:1:d:10.1007_s10203-017-0190-z
    DOI: 10.1007/s10203-017-0190-z
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    References listed on IDEAS

    as
    1. Radu Ioan Boţ & Ernö Robert Csetnek, 2013. "Conjugate Duality and the Control of Linear Discrete Systems," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 576-589, December.
    2. Radu Ioan Bot, 2010. "Conjugate Duality in Convex Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-04900-2, December.
    3. V. Jeyakumar, 2008. "Constraint Qualifications Characterizing Lagrangian Duality in Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 31-41, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Support function of a multifunction; Optimization over inclusions; Regularity conditions; Strong Lagrange duality; Stabilty; Conjugate duality; Discrete convex systems; Optimal control;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models

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