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A Continuous Method for Convex Programming Problems

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  • L. Z. Liao

    (Hong Kong Baptist University)

Abstract

In this paper, we present a continuous method for convex programming (CP) problems. Our approach converts first the convex problem into a monotone variational inequality (VI) problem. Then, a continuous method, which includes both a merit function and an ordinary differential equation (ODE), is introduced for the resulting variational inequality problem. The convergence of the ODE solution is proved for any starting point. There is no Lipschitz condition required in our proof. We show also that this limit point is an optimal solution for the original convex problem. Promising numerical results are presented.

Suggested Citation

  • L. Z. Liao, 2005. "A Continuous Method for Convex Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 207-226, January.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:1:d:10.1007_s10957-004-6473-x
    DOI: 10.1007/s10957-004-6473-x
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    References listed on IDEAS

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    1. B. S. He & L. Z. Liao, 2002. "Improvements of Some Projection Methods for Monotone Nonlinear Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 111-128, January.
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