IDEAS home Printed from https://ideas.repec.org/a/ibn/jmrjnl/v9y2017i4p168-184.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/view/69585/37866
    Download Restriction: no
    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/view/69585
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kuang Bai & Yixia Song & Jin Zhang, 2023. "Second-Order Enhanced Optimality Conditions and Constraint Qualifications," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1264-1284, September.
    2. Roberto Andreani & José Mario Martínez & Alberto Ramos & Paulo J. S. Silva, 2018. "Strict Constraint Qualifications and Sequential Optimality Conditions for Constrained Optimization," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 693-717, August.
    3. Enrico Bellino, 2010. "Comment To ‘Commodity Content . . .’ By Fujimoto And Opocher," Metroeconomica, Wiley Blackwell, vol. 61(4), pages 749-753, November.
    4. X. F. Li & J. Z. Zhang, 2006. "Necessary Optimality Conditions in Terms of Convexificators in Lipschitz Optimization," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 429-452, December.
    5. Y. Y. Zhou & X. Q. Yang, 2009. "Duality and Penalization in Optimization via an Augmented Lagrangian Function with Applications," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 171-188, January.
    6. Florian Scheuer & Alexander Wolitzky, 2016. "Capital Taxation under Political Constraints," American Economic Review, American Economic Association, vol. 106(8), pages 2304-2328, August.
    7. Abhishek Singh & Debdas Ghosh & Qamrul Hasan Ansari, 2024. "Inexact Newton Method for Solving Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 1333-1363, June.
    8. Casey Rothschild & Florian Scheuer, 2016. "Optimal Taxation with Rent-Seeking," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(3), pages 1225-1262.
    9. A. Pascoletti & P. Serafini, 2007. "Differential Conditions for Constrained Nonlinear Programming via Pareto Optimization," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 399-411, September.
    10. Sjur D. Flåm & Jan-J. Rückmann, 2022. "The Lagrangian, constraint qualifications and economics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(2), pages 215-232, October.
    11. Yuntong Wang, 2014. "Envelope Theorem without Differentiability," Working Papers 1404, University of Windsor, Department of Economics.
    12. Zachary Bethune & Tai-Wei Hu & Guillaume Rocheteau, 2018. "Optimal Credit Cycles," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 27, pages 231-245, January.
    13. 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.
    14. Ewald, Christian Oliver & Nolan, Charles, 2024. "On the adaptation of the Lagrange formalism to continuous time stochastic optimal control: A Lagrange-Chow redux," Journal of Economic Dynamics and Control, Elsevier, vol. 162(C).
    15. Elodie Adida & Georgia Perakis, 2007. "A nonlinear continuous time optimal control model of dynamic pricing and inventory control with no backorders," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(7), pages 767-795, October.
    16. Holger Scheel & Stefan Scholtes, 2000. "Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 1-22, February.
    17. Casey Rothschild & Florian Scheuer, 2014. "A Theory of Income Taxation under Multidimensional Skill Heterogeneity," NBER Working Papers 19822, National Bureau of Economic Research, Inc.
    18. Ronaldo C. Duarte, 2022. "Ground state solution for nonlocal scalar field equations involving an integro-differential operator," Partial Differential Equations and Applications, Springer, vol. 3(2), pages 1-14, April.
    19. 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.
    20. Nguyen Thi Hang & Jen-Chih Yao, 2016. "Sufficient conditions for error bounds of difference functions and applications," Journal of Global Optimization, Springer, vol. 66(3), pages 439-456, November.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ibn:jmrjnl:v:9:y:2017:i:4:p:168-184. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Canadian Center of Science and Education (email available below). General contact details of provider: https://edirc.repec.org/data/cepflch.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.