Proportionality-Based Gradient Methods with Applications in Contact Mechanics

  • Zdeněk Dostál
  • Gerardo Toraldo
  • Marco Viola
  • Oldřich VlachEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11087)


Two proportionality based gradient methods for the solution of large convex bound constrained quadratic programming problems, MPRGP (Modified Proportioning with Reduced Gradient Projections) and P2GP (Proportionality-based Two-phase Gradient Projection) are presented and applied to the solution of auxiliary problems in the inner loop of an augmented lagrangian algorithm called SMALBE (Semi-monotonic Augmented Lagrangian for Bound and Equality constraints). The SMALBE algorithm is used to generate the Lagrange multipliers for the equality constraints. The performance of the algorithms is tested on the solution of the discretized contact problems by means of TFETI (Total Finite Element Tearing and Interconnecting).


QP optimization Contact problems P2GP MPRGP 



This work was supported by The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPS II) project “IT4Innovations excellence in science - LQ1602” and by the IT4Innovations infrastructure which is supported from the Large Infrastructures for Research, Experimental Development and Innovations project “IT4Innovations National Supercomputing Center - LM2015070”. The work was partially supported by Gruppo Nazionale per il Calcolo Scientifico - Istituto Nazionale di Alta Matematica (GNCS-INdAM).


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Zdeněk Dostál
    • 1
    • 4
  • Gerardo Toraldo
    • 2
  • Marco Viola
    • 3
  • Oldřich Vlach
    • 1
    • 4
    Email author
  1. 1.Department of Applied Mathematics, Faculty of Electrical Engineering and Computer ScienceVŠB-Technical University of OstravaOstravaCzech Republic
  2. 2.Department of Mathematics and ApplicationsUniversity of Naples Federico IINaplesItaly
  3. 3.Department of Computer Control and Management EngineeringSapienza University of RomeRomeItaly
  4. 4.IT4Innovations, National Supercomputing CenterVŠB-Technical University of OstravaOstravaCzech Republic

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