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Matrix convex functions with applications to weighted centers for semidefinite programming

Author

Listed:
  • Brinkhuis, J.
  • Luo, Z-Q.
  • Zhang, S.

Abstract

In this paper, we develop various calculus rules for general smooth matrix-valued functions and for the class of matrix convex (or concave) functions first introduced by Loewner and Kraus in 1930s. Then we use these calculus rules and the matrix convex function -log X to study a new notion of weighted convex centers for semidefinite programming (SDP) and show that, with this definition, some known properties of weighted centers for linear programming can be extended to SDP. We also show how the calculus rules for matrix convex functions can be used in the implementation of barrier methods for optimization problems involving nonlinear matrix functions.

Suggested Citation

  • Brinkhuis, J. & Luo, Z-Q. & Zhang, S., 2005. "Matrix convex functions with applications to weighted centers for semidefinite programming," Econometric Institute Research Papers EI 2005-38, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:7025
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    More about this item

    Keywords

    matrix convexity; matrix monotonicity; semidefinite programming;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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