Dual optimality conditions for the difference of extended real valued increasing co-radiant functions. (English) Zbl 07925621
Summary: The aim of this paper is to present dual optimality conditions for the difference of two extended real valued increasing co-radiant functions. We do this by first characterizing dual optimality conditions for the difference of two nonpositive increasing co-radiant functions. Finally, we present dual optimality conditions for the difference of two extended real valued increasing co-radiant functions. Our approach is based on the Toland-Singer formula.
MSC:
26B25 | Convexity of real functions of several variables, generalizations |
26A48 | Monotonic functions, generalizations |
90C26 | Nonconvex programming, global optimization |
90C46 | Optimality conditions and duality in mathematical programming |
90C34 | Semi-infinite programming |
Keywords:
global optimization; abstract convexity; increasing co-radiant function; abstract subdifferential; support set; Toland-Singer formulaReferences:
[1] | Daryaei, MH; Mohebi, H., Abstract convexity of extended real valued ICR functions, Optimization, 62, 6, 835-855, 2013 · Zbl 1272.26006 · doi:10.1080/02331934.2012.741127 |
[2] | Daryaei, MH; Mohebi, H., Global minimization of the difference of strictly non-positive valued affine ICR functions, J. Global Optim., 61, 311-323, 2015 · Zbl 1339.90264 · doi:10.1007/s10898-014-0168-0 |
[3] | Doagooei, AR; Mohebi, H., Monotonic analysis over ordered topological vector spaces: IV, J. Global Optim., 45, 355-369, 2009 · Zbl 1200.26014 · doi:10.1007/s10898-008-9379-6 |
[4] | Doagooei, AR; Mohebi, H., Optimization of the difference of ICR functions, Nonlinear Anal., 71, 4493-4499, 2009 · Zbl 1178.90342 · doi:10.1016/j.na.2009.03.017 |
[5] | Glover, BM; Jeyakumar, V., Nonlinear extensions of Farkas’ lemma with applications to global optimization and least squares, Math. Oper. Res., 20, 818-837, 1995 · Zbl 0846.90098 · doi:10.1287/moor.20.4.818 |
[6] | Glover, BM; Ishizuka, Y.; Jeyakumar, V.; Rubinov, AM, Inequality systems and global optimization, J. Math. Anal. Appl., 202, 900-919, 1996 · Zbl 0856.90128 · doi:10.1006/jmaa.1996.0353 |
[7] | Hiriart-Urruty, J.B.: From convex to nonconvex minimization: necessary and sufficient conditions for global optimality. In: Nonsmooth Optimization and Related Topics, pp. 219-240. Plenum, New York (1989) |
[8] | Mohebi, H., Abstract convexity of radiant functions with applications, J. Global Optim., 55, 521-538, 2013 · Zbl 1263.26022 · doi:10.1007/s10898-012-9888-1 |
[9] | Mohebi, H.; Mirzadeh, S., Abstract convexity of extended real valued increasing and radiant functions, Filomat, 26, 5, 1005-1022, 2012 · Zbl 1289.26023 · doi:10.2298/FIL1205005M |
[10] | Mohebi, H.; Sadeghi, H., Monotonic analysis over ordered topological vector spaces: I, Optimization, 56, 3, 305-321, 2007 · Zbl 1144.26012 · doi:10.1080/02331930600819746 |
[11] | Mohebi, H.; Sadeghi, H., Monotonic analysis over ordered topological vector spaces: II, Optimization, 58, 2, 241-249, 2009 · Zbl 1158.26305 · doi:10.1080/02331930701761664 |
[12] | Nedić, A.; Ozdaglar, A.; Rubinov, AM, Abstract convexity for nonconvex optimization duality, Optimization, 56, 5, 655-674, 2007 · Zbl 1172.90465 · doi:10.1080/02331930701617379 |
[13] | Rubinov, AM, Abstract Convexity and Global Optimization, 2000, Dordrecht-Boston-London: Kluwer Academic Publishers, Dordrecht-Boston-London · Zbl 0985.90074 · doi:10.1007/978-1-4757-3200-9 |
[14] | Rubinov, AM; Glover, BM, Increasing convex-along-rays functions with application to global optimization, J. Optim. Theory Appl., 102, 3, 615-642, 1999 · Zbl 0955.90105 · doi:10.1023/A:1022602223919 |
[15] | Singer, I., Abstract Convex Analysis, 1997, New York: Wiley-Interscience, New York · Zbl 0898.49001 |
[16] | Zaffaroni, A., Is every radiant function the sum of quasiconvex functions?, Math. Meth. Oper. Res., 59, 221-233, 2004 · Zbl 1056.49020 · doi:10.1007/s001860300325 |
[17] | Zaffaroni, A., Superlinear separation and dual characterizations of radiant functions, Pacific J. Optim., 2, 181-202, 2006 · Zbl 1109.26010 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.