A sufficient optimality condition for nonregular problems via a nonlinear Lagrangian

A. C. Eberhard; C.E.M. Pearce

doi:10.3934/naco.2012.2.301

Article Contents

2012, Volume 2, Issue 2: 301-331. Doi: 10.3934/naco.2012.2.301

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A sufficient optimality condition for nonregular problems via a nonlinear Lagrangian

A. C. Eberhard^1, and
C.E.M. Pearce^2,

1.
School of Mathematical and Geospatial Sciences, Royal Melbourne Institute of Technology, G.P.O. Box 2476V, Melbourne, Australia 3001
2.
School of Mathematical Sciences, The University of Adelaide, Australia SA 5005

Received: November 30, 2011

Revised: April 30, 2012

Published: April 2012

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Abstract

A reformulation of a standard smooth mathematical program in terms of a nonlinear Lagrangian is used in conjunction with the calculus of subhessians to derive a set of sufficient optimality conditions that are applicable to some nonregular problems. These conditions are cast solely in terms of the first-- and second--order derivatives of the constituent functions and generalize standard second--order sufficiency conditions to a wide class of potentially nonregular problems.

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Mathematics Subject Classification: Primary: 90C46, 49J52; Secondary: 90C46.

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