Expanding the Reach of Nonlinear Optimization

Abstract

Affine variational inequalities (AVI) are an important problem class that generalize systems of linear equations, linear complementarity problems and optimality conditions for quadratic programs. Among other things, they are models for the equilibrium constraints used in MOPEC and MPEC, where the acronym MOPEC means multiple optimization problem with equilibrium constraints, and MPEC means mathematical program with equilibrium constraints. Therefore, solution methods for AVI are important elements in dealing with MOPEC and MPEC. The work done under this grant included development and testing of the algorithm PATHAVI, which uses a structure-preserving pivotal approach to process (solve or determine infeasible) large-scale sparse instances of an AVI problem efficiently, with theoretical guarantees and at high accuracy. PATHAVI implements a strategy that is known to process models with good theoretical properties without reducing the problem to specialized forms, since such reductions may destroy structure in the models and can lead to very long computational times.

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Document Details

Document Type
Technical Report
Publication Date
Aug 13, 2018
Accession Number
AD1059127

Entities

People

  • Michael C. Ferris
  • Stephen M. Robinson

Organizations

  • University of Wisconsin–Madison

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  • Energy and Power Technologies
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  • Materials and Manufacturing Processes

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