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  • Optimality  (1)
  • duality  (1)
  • projections  (1)
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  • 1
    Digitale Medien
    Digitale Medien
    Projection and restriction methods in geometric programming and related problems (1978)
    Springer
    Journal of optimization theory and applications 26 (1978), S. 59-76 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Geometric programming ; convex programming ; Slater condition ; projections ; restrictions ; duality
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Mathematical programming problems with unattained infima or unbounded optimal solution sets are dual to problems which lackinterior points, e.g., problems for which the Slater condition fails to hold or for which the hypothesis of Fenchel's theorem fails to hold. In such cases, it is possible to project the unbounded problem onto a subspace and to restrict the dual problem to an affine set so that the infima are not altered. After a finite sequence of such projections and restrictions, dual problems are obtained which have bounded optimal solution sets andinterior points. Although results of this kind have occasionally been used in other contexts, it is in geometric programming (both in the original psynomial form and the generalized form) where such methods appear most useful. In this paper, we present a treatment of dual projection and restriction methods developed in terms of dual generalized geometric programming problems. Analogous results are given for Fenchel and ordinary dual problems.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00933271
    Standort Signatur Erwartet Verfügbarkeit
    BibTip Andere fanden auch interessant ...
    Artikel (Nationallizenzen)
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  • 2
    Digitale Medien
    Digitale Medien
    A simplified test for optimality (1978)
    Springer
    Journal of optimization theory and applications 25 (1978), S. 161-170 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimality ; convex programming ; feasible directions ; cones of decrease ; cones of constancy
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract A simplification of recent characterizations of optimality in convex programming involving the cones of decrease and constancy of the objective and constraint functions is presented. In the original characterization due to Ben-Israelet al., optimality was verified or a feasible direction of decrease was determined by considering a number of sets equal to the number of subsets of the set of binding constraints. By first finding the set of constraints which is binding at every feasible point, it is possible to verify optimality or determine a feasible direction of decrease by considering a single set. In the case of faithfully convex functions, this set can be found by solving at mostp systems of linear equations and inequalities, wherep is the number of constraints.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00933262
    Standort Signatur Erwartet Verfügbarkeit
    BibTip Andere fanden auch interessant ...
    Artikel (Nationallizenzen)
    Volltext
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