×

Programming with semilocally convex functions. (English) Zbl 0762.90064

Summary: A theorem of the alternatives is derived for semilocally convex functions defined on locally starshaped sets. This result is applied to constrained minimization problems to obtain optimality conditions and duality theorems.

MSC:

90C26 Nonconvex programming, global optimization
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Avriel, M; Diewert, W.E; Schaible, S; Zang, I, Generalized concavity, () · Zbl 0483.26007
[2] Craven, B.D, Mathematical programming and control theory, (1978), Chapman & Hall London · Zbl 0431.90039
[3] Ewing, G.M, Sufficient conditions for global minima of suitably convex functions from variational and control theory, SIAM rev., 19, 202-220, (1977) · Zbl 0361.49011
[4] Kaul, R.N; Kaur, S, Generalisations of convex and related functions, European J. oper. res., 9, 369-377, (1982) · Zbl 0501.90090
[5] Kaur, S, Theoretical studies in mathematical programming, ()
[6] Kuhn, H.W; Tucker, A.W, Nonlinear programming, (), 481-493 · Zbl 0044.05903
[7] John, F, Extremum problems with inequalities as subsidiary condtions, ()
[8] Werner, J, Optimization theory and applications, (1984), Vieweg Braunschweig
[9] Wolfe, P, A duality theorem for nonlinear programming, Quart. appl. math., 19, 239-244, (1961) · Zbl 0109.38406
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.