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F. A. Valentine, “The Problem of Lagrange with Differential Inequalities as Added Side Conditions, Contribution to the Calculus of Variation, 1933-1937,” University of Chicago Press, Chicago, 1937, pp. 407-448.

has been cited by the following article:

• TITLE: Sufficient Fritz John Type Optimality Criteria and Duality for Control Problems

  AUTHORS: Iqbal Husain, Santosh K. Srivastav

  KEYWORDS: Sufficient Optimality Criteria; Control Problem; Fritz John Type Dual; Nonlinear Programming Problem; Generalized Convexity

  JOURNAL NAME: American Journal of Industrial and Business Management, Vol.3 No.2, April 25, 2013

  ABSTRACT: Sufficient Fritz John optimality conditions are obtained for a control problem in which objective functional is pseudoconvex and constraint functions are quasiconvex or semi-strictly quasiconvex. A dual to the control problem is formulated using Fritz John type optimality criteria instead of Karush-Kuhn-Tucker optimality criteria and hence does not require a regularity condition. Various duality results amongst the control problem and its proposed dual are validated under suitable generalized convexity requirements. The relationship of our duality results to those of a nonlinear programming problem is also briefly outlined.