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A modified homogeneous potential reduction algorithm for solving the monotone semidefinite linear complementarity problem

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Abstract

In this paper, we study the performance of the Semidefinite Linear Complementarity Problem (SDLCP) for symmetric matrices that is equipped with a continuously differentiable potential function. A practical homogeneous self-dual potential reduction algorithm based on this potential function is prescribed, and we establish a computational basis for interior point methods with the use of HKM directions towards the central trajectory for the monotone SDLCP. Our computational implementation maintains a global linear polynomial time convergence, while achieving strong practical performance in comparison with existing solution methods.

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Authors and Affiliations

  1. Department of Mathematics, IIIT Bhubaneswar, Bhubaneswar, 751003, India

    Rupaj Kumar Nayak

  2. School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore, 639798, Singapore

    Jitamitra Desai

Authors
  1. Rupaj Kumar Nayak
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  2. Jitamitra Desai
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Correspondence to Jitamitra Desai.

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Nayak, R.K., Desai, J. A modified homogeneous potential reduction algorithm for solving the monotone semidefinite linear complementarity problem. Optim Lett 10, 1417–1448 (2016). https://doi.org/10.1007/s11590-015-0940-1

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