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An Outer Approximation Algorithm for Solving General Convex Programs

Author

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  • Masao Fukushima

    (Kyoto University, Kyoto, Japan)

Abstract

A new outer approximation algorithm is proposed for solving general convex programs. A remarkable advantage of the algorithm over existing outer approximation methods is that the approximation of the constraint set is not cumulative. That is, the algorithm solves at each iteration a quadratic program whose constraints depend only on the current estimate of an optimal solution. Convergence of the algorithm is proved and possible applications are discussed.

Suggested Citation

  • Masao Fukushima, 1983. "An Outer Approximation Algorithm for Solving General Convex Programs," Operations Research, INFORMS, vol. 31(1), pages 101-113, February.
    • Handle: RePEc:inm:oropre:v:31:y:1983:i:1:p:101-113
    DOI: 10.1287/opre.31.1.101
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    Cited by:

    1. Brito, A.S. & Cruz Neto, J.X. & Santos, P.S.M. & Souza, S.S., 2017. "A relaxed projection method for solving multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 256(1), pages 17-23.
    2. R. Behling & A. Fischer & M. Herrich & A. Iusem & Y. Ye, 2014. "A Levenberg-Marquardt method with approximate projections," Computational Optimization and Applications, Springer, vol. 59(1), pages 5-26, October.
    3. Phan Vuong & Jean Strodiot & Van Nguyen, 2014. "Projected viscosity subgradient methods for variational inequalities with equilibrium problem constraints in Hilbert spaces," Journal of Global Optimization, Springer, vol. 59(1), pages 173-190, May.
    4. J. Bello Cruz & A. Iusem, 2010. "Convergence of direct methods for paramonotone variational inequalities," Computational Optimization and Applications, Springer, vol. 46(2), pages 247-263, June.
    5. Reiner Horst, 1990. "Deterministic methods in constrained global optimization: Some recent advances and new fields of application," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 433-471, August.
    6. Bello Cruz, J.Y. & Iusem, A.N., 2015. "Full convergence of an approximate projection method for nonsmooth variational inequalities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 114(C), pages 2-13.

    More about this item

    Keywords

    642; 644 outer approximation algorithm;

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