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An Iterative Approach to Quadratic Optimization

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  • H.K. Xu

    (University of Durban-Westville)

Abstract

Assume that C 1, . . . , C N are N closed convex subsets of a real Hilbert space H having a nonempty intersection C. Assume also that each C i is the fixed point set of a nonexpansive mapping T i of H. We devise an iterative algorithm which generates a sequence (x n ) from an arbitrary initial x 0∈H. The sequence (xn) is shown to converge in norm to the unique solution of the quadratic minimization problem min x∈C (1/2)〈Ax, x〉−〈x, u〉, where A is a bounded linear strongly positive operator on H and u is a given point in H. Quadratic–quadratic minimization problems are also discussed.

Suggested Citation

  • H.K. Xu, 2003. "An Iterative Approach to Quadratic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 659-678, March.
    • Handle: RePEc:spr:joptap:v:116:y:2003:i:3:d:10.1023_a:1023073621589
    DOI: 10.1023/A:1023073621589
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    References listed on IDEAS

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    1. H. K. Xu & T. H. Kim, 2003. "Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 185-201, October.
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