# American Institute of Mathematical Sciences

2012, 2(2): 301-331. doi: 10.3934/naco.2012.2.301

## A sufficient optimality condition for nonregular problems via a nonlinear Lagrangian

 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  December 2011 Revised  May 2012 Published  May 2012

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.
Citation: A. C. Eberhard, C.E.M. Pearce. A sufficient optimality condition for nonregular problems via a nonlinear Lagrangian. Numerical Algebra, Control & Optimization, 2012, 2 (2) : 301-331. doi: 10.3934/naco.2012.2.301
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