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Projection and Rescaling Algorithm for Finding Maximum Support Solutions to Polyhedral Conic Systems

Author

Listed:
  • Javier Peña

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • Negar Soheili

    (College of Business Administration, University of Illinois at Chicago, Chicago, Illinois 60607)

Abstract

We propose a simple projection and rescaling algorithm that finds maximum support solutions to the pair of feasibility problems: find x ∈ L ∩ R + n and find x ^ ∈ L ⊥ ∩ R + n , where L is a linear subspace in R n and L ⊥ is its orthogonal complement. The algorithm complements a basic procedure that involves only projections onto L and L ⊥ with a periodic rescaling step. The number of rescaling steps and, thus, overall computational work performed by the algorithm are bounded above in terms of a condition measure of the above pair of problems. Our algorithm is a natural but significant extension of a previous projection and rescaling algorithm that finds a solution to the full support problem: find x ∈ L ∩ R + + n when this problem is feasible. As a byproduct of our new developments, we obtain a sharper analysis of the projection and rescaling algorithm in the latter special case.

Suggested Citation

  • Javier Peña & Negar Soheili, 2022. "Projection and Rescaling Algorithm for Finding Maximum Support Solutions to Polyhedral Conic Systems," Mathematics of Operations Research, INFORMS, vol. 47(4), pages 3304-3316, November.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:4:p:3304-3316
    DOI: 10.1287/moor.2021.1235
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