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AnO(n 2) active set method for solving a certain parametric quadratic program

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Abstract

This paper presents anO(n 2) method for solving the parametric quadratic program

$$\min (1/2)x'Dx - a'x + (\lambda /2)\left( {\sum\limits_{j = 1}^n {\gamma _j x_j } - c} \right)^2 ,$$

having lower and upper bounds on the variables, for all nonnegative values of the parameter λ. Here,D is a positive diagonal matrix,a an arbitraryn-vecotr, each γ j ,j=1, ...,n, andc are arbitrary scalars. An application to economics is also presented.

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Author notes

  1. N. Chakravarti (Assistant Professor)

    Present address: Operations Management Group, Indian Institute of Management, Calcutta, India

Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada

    M. J. Best (Professor Assistant Professor)

  2. Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois

    N. Chakravarti (Assistant Professor)

Authors
  1. M. J. Best
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  2. N. Chakravarti
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Additional information

Communicated by D. F. Shanno

The authors wish to thank Professor T. Nguyen, Department of Economics, University of Waterloo, for directing their attention to tax programming models.

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Best, M.J., Chakravarti, N. AnO(n 2) active set method for solving a certain parametric quadratic program. J Optim Theory Appl 72, 213–224 (1992). https://doi.org/10.1007/BF00940516

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