عنوان

Second-order sensitivity analysis in mathematical programming

Number

TLpq303770338

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

Second-order sensitivity analysis in mathematical programming

General Material Designation

[Thesis]

First Statement of Responsibility

C. Nahum

Name of Publisher, Distributor, etc.

McGill University (Canada)

Date of Publication, Distribution, etc.

1989

Specific Material Designation and Extent of Item

233

Dissertation or thesis details and type of degree

Ph.D.

Body granting the degree

McGill University (Canada)

Text preceding or following the note

1989

Text of Note

We consider a nonlinear mathematical program, with twice continuously differentiable functions. If a point x0 does not satisfy a certain Second Order Sufficient Condition (SOS) for optimality (that does not require any constraint qualification, see, e.g., BEN-ISRAEL, BEN-TAL and ZLOBEC (81)), then we prove that the knowledge of the second order properties (derivative, Hessian) of the functions is not enough to conclude that the point is optimal. When the functions are continuously perturbed, what is the local behavior of an optimal solution x0 and of the associate optimal value? The stability and sensitivity of the mathematical model are addressed. We present a new method for solving this problem. Our approach does not rely on the classical Lagrangian coefficients (which cannot be always defined) but rather on power series expansions because we use the primal formulations of optimality. In the regular case, when Strict complementarity slackness holds, we recover Fiacco's results (FIACCO (83)). On the other hand, when Strict complementarity slackness does not hold, we extensively generalize Shapiro's Theorems (SHAPIRO (85)) since we do not assume Robinson's second order condition (ROBINSON (80)) but the SOS condition. In the non-regular case, no general algorithm for computing the derivative of the optimizing point with respect to the parameters had been presented up to now. The approach is extended to analyze the evolution of the set of Pareto minima of a multiobjective nonlinear program. In particular, we define the derivative of a point-to-set map. Our notion seems more adequate than the contingent derivative (AUBIN (81)), though the latter can easily be deduced from the former. This allows to get information about the sensitivity of the set of Pareto minima. A real-life example shows the usefulness and the simplicity of our results. Also, an application of our method to industry planning (within a general framework of Input Optimization) is made in the ideal case of a linear model.

Applied sciences

Computer science

Mathematics

Mathematics

Pure sciences

C. Nahum

Electronic name

p

[Thesis]

276903

a

Y