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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 65, 2016 - Issue 4
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Articles

A full-Newton step infeasible interior-point method for linear optimization based on a trigonometric kernel function

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Pages 841-857 | Received 17 Nov 2014, Accepted 20 Jul 2015, Published online: 01 Sep 2015

References

  • Roos C, Terlaky T, Vial J-Ph. Theory and algorithms for linear optimization. An interior-point approach. Chichester: Wiley; 1997.
  • Lustig IJ. Feasible issues in a primal--dual interior-point method for linear programming. Math. Program. 1990;67:145–162.
  • Kojima M, Megiddo N, Mizuno S. A primal--dual infeasible-interior-point algorithm for linear programming. Math. Program. 1993;61:263–280.
  • Zhang Y. On the convergence of a class of infeasible interior-point methods for the horizontal linear complementarity problem. SIAM J. Optim. 1994;4:208–227.
  • Mizuno S. Polynomiality of infeasible-interior-point algorithms for linear programming. Math. Program. 1994;67:109–119.
  • Roos C. A full-newton step O(n) infeasible interior-point algorithm for linear optimization. SIAM J. Optim. 2006;16:1110–1136.
  • Kojima M, Megiddo N, Noma T, Yoshise A. A unified approach to interior point algorithms for linear complementarity problems. Vol. 538, Lecture Notes in Computer Science. Berlin: Springer-Verlag; 1991.
  • Potra FA. An O(nL) infeasible-interior-point algorithm for LCP with quadratic convergence. Ann. Oper. Res. 1996;62:81–102.
  • Peng J, Roos C, Terlaky T. Self-regular functions and new search directions for linear and semidefinite optimization. Math. Program. 2002;93:129–171.
  • Kheirfam B, Moslemi M. A polynomial-time algorithm for linear optimization based on a new kernel function with trigonometric barrier term. Yugosl. J. Oper. Res. 2015;25:233–250.
  • Liu Z, Sun W, Tian F. A full-Newton step infeasible interior-point algorithm for linear programming based on a kernel function. Appl. Math. Optim. 2009;60:237–251.
  • Kheirfam B. A full-Newton step infeasible interior-point algorithm for linear complementarity problems based on a kernel function. Algor. Oper. Res. 2013;7:103–110.
  • Kheirfam B. A full Nesterov-Todd step infeasible interior-point algorithm for symmetric optimization based on a specific kernel function. Numer. Algebra Contr. Optim. 2013;3:601–614.
  • Kheirfam B, Hasani F. A full-Newton step infeasible interior point method for linear optimization based on an exponential kernel function. Asian-European J. Math. 2014;7:1450018 (14p).
  • Darvay Z. New interior point algorithm in linear programming. Adv. Model. Optim. 2003;5:51–92.
  • Qi F. Jordan’s inequality: refinements, generalizations, applications and related problems. RGMIA Res. Rep. Coll. 2006;9:12 (16p) (electronic). Budengshi Yanjiu Tongxun (Communications in Studies on Inequalities) 2006;13:243–259.
  • Mitrinović DS. Analytic inequalities. New York (NY): Springer Verlag; 1970.
  • Liu Z, Chen Y. A full-Newton step infeasible interior-point algorithm for linear programmig based on a self-regular proximity. J. Appl. Math. Informatics. 2011;29:119–133.

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