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An exterior point polynomial-time algorithm for convex quadratic programming

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  • Da Tian

Abstract

In this paper an exterior point polynomial time algorithm for convex quadratic programming problems is proposed. We convert a convex quadratic program into an unconstrained convex program problem with a self-concordant objective function. We show that, only with duality, the Path-following method is valid. The computational complexity analysis of the algorithm is given. Copyright Springer Science+Business Media New York 2015

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  • Da Tian, 2015. "An exterior point polynomial-time algorithm for convex quadratic programming," Computational Optimization and Applications, Springer, vol. 61(1), pages 51-78, May.
    • Handle: RePEc:spr:coopap:v:61:y:2015:i:1:p:51-78
    DOI: 10.1007/s10589-014-9710-8
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    References listed on IDEAS

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    1. Da Tian, 2014. "An entire space polynomial-time algorithm for linear programming," Journal of Global Optimization, Springer, vol. 58(1), pages 109-135, January.
    2. S. C. Fang & H. S. J. Tsao, 1997. "Perturbing the Dual Feasible Region for Solving Convex Quadratic Programs," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 73-85, July.
    3. Zhongyi Liu & Yue Chen & Wenyu Sun & Zhihui Wei, 2012. "A Predictor-corrector algorithm with multiple corrections for convex quadratic programming," Computational Optimization and Applications, Springer, vol. 52(2), pages 373-391, June.
    4. Quoc Tran Dinh & Ion Necoara & Moritz Diehl, 2014. "Path-following gradient-based decomposition algorithms for separable convex optimization," Journal of Global Optimization, Springer, vol. 59(1), pages 59-80, May.
    5. Sanjay Mehrotra & Jie Sun, 1990. "An Algorithm for Convex Quadratic Programming That Requires O ( n 3.5 L ) Arithmetic Operations," Mathematics of Operations Research, INFORMS, vol. 15(2), pages 342-363, May.
    6. Jin Jung & Dianne O’Leary & André Tits, 2012. "Adaptive constraint reduction for convex quadratic programming," Computational Optimization and Applications, Springer, vol. 51(1), pages 125-157, January.
    7. Yang, Yaguang, 2011. "A polynomial arc-search interior-point algorithm for convex quadratic programming," European Journal of Operational Research, Elsevier, vol. 215(1), pages 25-38, November.
    8. A. D. Martin, Jr., 1955. "Mathematical Programming of Portfolio Selections," Management Science, INFORMS, vol. 1(2), pages 152-166, January.
    9. R. Polyak & I. Griva, 2004. "Primal-Dual Nonlinear Rescaling Method for Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 111-156, July.
    10. J. Burke & S. Xu, 2002. "Complexity of a Noninterior Path-Following Method for the Linear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 53-76, January.
    11. I. Necoara & J. A. K. Suykens, 2009. "Interior-Point Lagrangian Decomposition Method for Separable Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 567-588, December.
    12. Ben-Daya, M. & Al-Sultan, K. S., 1997. "A new penalty function algorithm for convex quadratic programming," European Journal of Operational Research, Elsevier, vol. 101(1), pages 155-163, August.
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    1. Assalé Adjé, 2021. "Quadratic Maximization of Reachable Values of Affine Systems with Diagonalizable Matrix," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 136-163, April.

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