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Minimum Principle-Type Necessary Optimality Conditions in Scalar and Vector Optimization. An Account

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  • Giorgio Giorgi

Abstract

We take into condideration necessary optimality conditions of minimum principle-type, that is for optimization problems having, besides the usual inequality and/or equality constraints, a set constraint. The first part pf the paper is concerned with scalar optimization problems; the second part of the paper deals with vector optimization problems.

Suggested Citation

  • Giorgio Giorgi, 2017. "Minimum Principle-Type Necessary Optimality Conditions in Scalar and Vector Optimization. An Account," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(4), pages 168-184, August.
    • Handle: RePEc:ibn:jmrjnl:v:9:y:2017:i:4:p:168-184
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    References listed on IDEAS

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    1. Fabián Flores-Bazán, 2014. "Fritz John Necessary Optimality Conditions of the Alternative-Type," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 807-818, June.
    2. D. H. Martin & G. G. Watkins, 1985. "Cores of Tangent Cones and Clarke's Tangent Cone," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 565-575, November.
    3. Giorgio Giorgi & Cesare Zuccotti, 2012. "On the use of some tangent cones and sets in vector optimization," Quaderni di Dipartimento 169, University of Pavia, Department of Economics and Quantitative Methods.
    4. D.P. Bertsekas & A.E. Ozdaglar, 2002. "Pseudonormality and a Lagrange Multiplier Theory for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 287-343, August.
    5. Frank H. Clarke, 1976. "A New Approach to Lagrange Multipliers," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 165-174, May.
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    Cited by:

    1. Giorgio Giorgi, 2018. "A Guided Tour in Constraint Qualifications for Nonlinear Programming under Differentiability Assumptions," DEM Working Papers Series 160, University of Pavia, Department of Economics and Management.

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    More about this item

    Keywords

    Minimum principle-type conditions; optimality conditions; set constraint; scalar optimization; vector optimization;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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