×

zbMATH — the first resource for mathematics

Surrogate dual problems and surrogate Lagrangians. (English) Zbl 0584.49006
The author continues his study of perturbed quasiconvex duality. Various new results on surrogate Lagrangians are given and specializations are considered.

MSC:
49N15 Duality theory (optimization)
49J45 Methods involving semicontinuity and convergence; relaxation
90C48 Programming in abstract spaces
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Borwein, J, Multivalued convexity and optimization: A unified approach to inequality and equality constraints, Math. progr., 13, 183-199, (1977) · Zbl 0375.90062
[2] Crouzeix, J.-P, Contributions à l’étude des fonctions quasiconvexes, ()
[3] Dixmier, J, Sur un théorème de Banach, Duke math. J., 15, 1057-1071, (1948) · Zbl 0031.36301
[4] Dolecki, S; Kurcyusz, S, On φ-convexity in extremal problems, SIAM J. control optim., 16, 277-300, (1978) · Zbl 0397.46013
[5] Ekeland, I; Temam, R, Analyse convexe et problèmes variationnels, (1974), Dunod-Gauthier Villars Paris · Zbl 0281.49001
[6] Glover, F, A multiphase-dual algorithm for the zero-one integer programming problem, Oper. res., 13, 879-919, (1965) · Zbl 0163.41301
[7] Greenberg, H.J; Pierskalla, W.P, Surrogate mathematical programming, Oper. res., 18, 924-939, (1970) · Zbl 0232.90059
[8] Greenberg, H.J; Pierskalla, W.P, Quasi-conjugate functions and surrogate duality, Cahiers centre études rech. opér., 15, 437-448, (1973) · Zbl 0276.90051
[9] Joly, J.-L; Laurent, P.-J, Stability and duality in convex minimization problems, Rev. franç. inf. rech. opér. R-2, 5, 3-42, (1971) · Zbl 0261.90051
[10] Kurcyusz, S, Some remarks on generalized Lagrangians, (), 363-388 · Zbl 0362.90100
[11] Laurent, P.-J, Approximation et optimisation, (1972), Hermann Paris · Zbl 0238.90058
[12] Luenberger, D.G, Quasi-convex programming, SIAM J. appl. math., 16, 1090-1095, (1968) · Zbl 0212.23905
[13] Luenberger, D.G, Optimization by vector space methods, (1969), New York/London/ Sydney/Toronto · Zbl 0176.12701
[14] \scW. Oettli, Optimality conditions involving generalized convex mappings, in “Proc. Advanced Study Inst. on Generalized Concavity in Optimization and Economics,” to appear. · Zbl 0538.90080
[15] Rockafellar, R.T, Convex functions and duality in optimization problems and dynamics, (), 117-141 · Zbl 0186.23901
[16] Rockafellar, R.T, Conjugate duality and optimization, () · Zbl 0186.23901
[17] Rolewicz, S, On a problem of moments, Studia math., 30, 183-191, (1968) · Zbl 0159.43802
[18] Rolewicz, S, Analiza funkcjonalna i teoria sterowania, (1974), PWN Warszawa · Zbl 0333.49001
[19] German translation, Springer-Verlag, Berlin/Heidelberg/New York, 1976.
[20] Rolewicz, S, On general theory of linear systems, Beiträge anal., 8, 119-127, (1976)
[21] Singer, I, On a problem of moments of S. rolewicz, Studia math., 68, 95-98, (1973) · Zbl 0265.47004
[22] Singer, I, Generalization of methods of best approximation to convex optimization in locally convex spaces. II: hyperplane theorems, J. math. anal. appl., 69, 571-584, (1979) · Zbl 0466.41013
[23] Singer, I, Some new applications of the Fenchel-rockafellar duality theorem: Lagrange multiplier theorems and hyperplane theorems for convex optimization and best approximation, Nonlinear anal. theory, methods appl., 3, 239-248, (1979) · Zbl 0444.41015
[24] Singer, I, On the Pontryagin maximum principle for constant-time linear control systems in Banach spaces, J. optim. theory appl., 27, 325-331, (1979)
[25] Singer, I, Maximization of lower semi-continuous convex functionals on bounded subsets of locally convex spaces. II: quasi-Lagrangian duality theorems, Resultate math., 3, 235-248, (1980) · Zbl 0459.90088
[26] Singer, I, Duality theorems for linear systems and convex systems, J. math. anal. appl., 76, 339-368, (1980) · Zbl 0445.49007
[27] Singer, I, Duality theorems for constrained convex optimization, Control cybernetics, 9, 37-45, (1980) · Zbl 0526.49009
[28] Singer, I, A characterization of constant-time linear control systems satisfying the Pontryagin maximum principle, J. optim. theory appl., 32, 379-384, (1980) · Zbl 0442.49015
[29] Singer, I, Duality theorems for perturbed convex optimization, J. math. anal. appl., 81, 437-452, (1981) · Zbl 0462.90091
[30] Singer, I, On the perturbation and Lagrangian duality theories of rockafellar and kurcyusz, (), 153-156 · Zbl 0467.90077
[31] Singer, I, Pseudo-conjugate functionals and pseudo-duality, (), 115-134
[32] Singer, I, Optimization by level set methods. I: duality formulae, (), in press · Zbl 0522.49010
[33] \scI. Singer, Abstract Pontryagin maximum principles for linear systems, Linear and Multilinear Algebra, in press. · Zbl 0529.49010
[34] \scI. Singer, Optimization by level set methods. IV: Generalizations and complements, to appear. · Zbl 0497.49022
[35] Zabotin, Ya.I; Korablev, A.I; Habibullin, R.F, Conditions for an extremum of a functional in the presence of constraints, Kibernetika, No. 6, 65-79, (1973), [Russian]
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.