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MPGP and PBBF for Separable QCQP

In: Optimal Quadratic Programming and QCQP Algorithms with Case Studies

Author

Listed:
  • Zdeněk Dostál

    (VŠB - Technical University Ostrava, National Super computer Center and Department of Applied Mathematics)

Abstract

We describe the MPGP (modified proportioning with gradient projection) algorithm for solving quadratic programming problems with separable constraints. The algorithm combines the conjugate gradient steps to minimize the cost function in the face with gradient projection steps to change the face. The decision on which step to use depends on violating the KKT conditions. The MPGP algorithm enjoys the R-linear rate of convergence of both the cost function and norm of projected gradient. We also present an alternative PBBF algorithm using projected Barzilai–Borwein steps with fallback. The performance of the algorithms, including scalability, is illustrated by solving a contact problem with anisotropic Coulomb friction.

Suggested Citation

  • Zdeněk Dostál, 2025. "MPGP and PBBF for Separable QCQP," Springer Optimization and Its Applications, in: Optimal Quadratic Programming and QCQP Algorithms with Case Studies, edition 0, chapter 0, pages 249-269, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-95167-1_11
    DOI: 10.1007/978-3-031-95167-1_11
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