A project Submitted in partial fulfllment of the requirements of the degree of master of science in mathematics
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Date
2014-06
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Addis Ababa University
Abstract
In this project work a smooth parametric nonlinear optimization problems subject to equality
and inequality constraints are considered. Emphasis is given on those conditions under
which the optimal solutions are di_erentiable functions of parameters. In theory these conditions
are related to regularity conditions and to second order su_cient conditions. The
interest in conditions for solution di_erentiability originates in the real-time computation
(approximation) of perturbed optimal solutions under parameter changes through _rst order
Taylor expansions. We study the explicit formulae and methods for computing for the
sensitivity derivatives of the solution vector and the associated multipliers with respect to
parameters. We discuss post-optimal evaluations of sensitivity derivatives and their numerical
implementation. The purpose of this work is to describe the application of sensitivity
analysis to approximate perturbed solutions in view of optimality and admissibility by using
Taylor expansion and extend the sensitivity theory to provide a complete map of the optimal
solution in the space of varying parameters for the case of multi-parametric quadratic
programming(mpQP).
Keywords. Nonlinear Optimization, Parametric nonlinear programming, Parametric quadratic
programming
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Keywords
Nonlinear Optimization, Parametric Nonlinear Programming, Parametric Quadratic Programming