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-factor methods for nonregular inequality-constrained optimization problems

✍ Scribed by Ewa Szczepanik; Alexey Tret’yakov

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
547 KB
Volume
69
Category
Article
ISSN
0362-546X

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✦ Synopsis

The paper presents a new method for solving irregular optimization problems with inequality constraints. Our results are based on the construction of p-regularity theory and on reformulating the inequality constraints as equalities. Namely, by introducing the slack variables of corresponding degree we obtain the equality-constrained problem, where their gradients are linearly dependent, and for which the Lagrange optimality system is singular at the solution of the optimization problem. We have derived the p-factor Lagrange system for finding extremum point x * , and under new sufficient condition of nondegeneracy in singular case we have proved regularity of this p-factor Lagrange system at solution point (x * , y * , λ * ). At the end, we presented numerical scheme for general case.

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