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Title: On some contributions to optimality conditions and duality in mathematical programming
Researcher: Shrivastav, Santosh Kumar
Guide(s): HUSAIN, I
Keywords: Generalized Second-Order Duality
Mathematical Programming
Nonlinear Programming
Upload Date: 7-May-2014
University: Jaypee University of Engineering and Technology, Guna
Completed Date: 20/12/2013
Abstract: The thesis comprises seven chapters and the gist of each chapter is given below:The first chapter is an introductory one and contains a brief survey of related literature,preliminaries and summary of the research work presented in the thesis. newlineIn the second chapter, we obtain optimality conditions for a class of non differentiable nonlinear programming problems with equality and inequality constraints in which the objective contains the square root of a positive semi definite quadratic function and is ,therefore, not differentiable. Using Karush-Kuhn-Tucker optimality conditions, Mond-Weir dual to this problem is constructed and various duality results are validated under suitable generalized invexity newlinehypotheses. A mixed type dual to the problem is also formulated and duality results are similarly derived. newlineIn the third chapter, a dual for a nonlinear programming problem in the presence of equality and inequality constraints which represent many realistic situations is formulated using Fritz John optimality conditions instead of the Karush-Kuhn-Tucker optimality conditions and hence does not require a constraint qualification. Various duality results, namely, weak, strong, strict newlineconverse and converse duality theorems are established under suitable generalized convexity. A generalized Fritz John type dual to the problem is also formulated and usual duality results are proved. In essence, the duality results do not require any regularity condition if the formulations newlineof dual problems use Fritz John optimality conditions. newlineIn the fourth chapter, 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 pseudoconvex. 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.
Appears in Departments:Department of Mathematics

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02_certificates.pdf69.03 kBAdobe PDFView/Open
03_abstract.pdf15.59 kBAdobe PDFView/Open
04_declaration.pdf6.29 kBAdobe PDFView/Open
05_acknowledgement.pdf39.64 kBAdobe PDFView/Open
06_contents.pdf13.96 kBAdobe PDFView/Open
10_chapter4.pdf194.7 kBAdobe PDFView/Open
11_chapter5.pdf224.86 kBAdobe PDFView/Open
12_chapter6.pdf128.15 kBAdobe PDFView/Open
13_chapter7.pdf306.17 kBAdobe PDFView/Open
14_bibliography.pdf40.37 kBAdobe PDFView/Open
15_list of publication.pdf8.88 kBAdobe PDFView/Open
7_chapter1.pdf266.95 kBAdobe PDFView/Open
8_chapter2.pdf206.06 kBAdobe PDFView/Open
9_chapter3.pdf138.84 kBAdobe PDFView/Open

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