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A critical index algorithm for nearest point problems on simplicial cones

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Abstract

We consider the linear complementarity problem (q, M) in whichM is a positive definite symmetric matrix of ordern. This problem is equivalent to a nearest point problem [Γ; b] in whichΓ = {A.1,⋯, A. n } is a basis for Rn,b is a given point in Rn; and it is required to find the nearest point in the simplicial cone Pos(Γ) tob. We develop an algorithm for solving the linear complementarity problem (q, M) or the equivalent nearest point problem [Γ; b]. Computational experience in comparison with an existing algorithm is presented.

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Authors and Affiliations

  1. Department of Industrial and Operations Engineering, University of Michigan, 48019, Ann Arbor, MI, USA

    Katta G. Murty

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, 30332, Atlanta, GA, USA

    Yahya Fathi

Authors
  1. Katta G. Murty
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  2. Yahya Fathi
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Additional information

Research effort partially supported by the Air Force Office of Scientific Research. Air Force Systems Command, USAF, under grant No. AFOSR 78-3646. The United States Government is authorized to reproduce and distribute reprints for governmental purposes, not withstanding any copyright notation hereon.

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Murty, K.G., Fathi, Y. A critical index algorithm for nearest point problems on simplicial cones. Mathematical Programming 23, 206–215 (1982). https://doi.org/10.1007/BF01583789

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  • DOI: https://doi.org/10.1007/BF01583789

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