Bifurcation analysis for singularities on a tangent space for quadratic penalty-barrier and multipliers methods for solving constrained optimization problems, part I

Mohammed A. Hasan, Aubrey B. Poore

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Abstract

The structure and persistence of critical point solutions obtained from solving constrained optimization problem by the quadratic penalty, the logarithmic-barrier functions, and the multiplier methods are analyzed. This analysis is mainly concerned with singularities due to the Hessian of the Lagrangian being singular on a tangent space. Formulation of the first order conditions of optimality into an algebraic system of equations is first established. The singularities of this system are then classified and solutions are investigated at singularities of codimensions zero and one in terms of the bifurcation behavior and persistence of the curve of critical points.

Original languageEnglish (US)
Pages (from-to)658-678
Number of pages21
JournalJournal of Mathematical Analysis and Applications
Volume197
Issue number3
DOIs
StatePublished - Feb 1 1996

Bibliographical note

Funding Information:
* This work was supported under the following grants: NFS Grant _ aDMS-87-04679, Air Force Grants AFOSR-88-0059, and AFOSR-91-0138.

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