A Project Submitted In Partial Fulfllment Of The Requirements Of The Degree Of Master Of Science In Mathematics

In this project work a smooth parametric nonlinear optimization problems subject to equalityrnand inequality constraints are considered. Emphasis is given on those conditions underrnwhich the optimal solutions are di_erentiable functions of parameters. In theory these conditionsrnare related to regularity conditions and to second order su_cient conditions. Therninterest in conditions for solution di_erentiability originates in the real-time computationrn(approximation) of perturbed optimal solutions under parameter changes through _rst orderrnTaylor expansions. We study the explicit formulae and methods for computing for thernsensitivity derivatives of the solution vector and the associated multipliers with respect tornparameters. We discuss post-optimal evaluations of sensitivity derivatives and their numericalrnimplementation. The purpose of this work is to describe the application of sensitivityrnanalysis to approximate perturbed solutions in view of optimality and admissibility by usingrnTaylor expansion and extend the sensitivity theory to provide a complete map of the optimalrnsolution in the space of varying parameters for the case of multi-parametric quadraticrnprogramming(mpQP).rnKeywords. Nonlinear Optimization, Parametric nonlinear programming, Parametric quadraticrnprogramming

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