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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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Additional information

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

Communicated by D. F. Shanno

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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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Key Words

  • Strong polynomiality
  • active set methods
  • tax programming models