Corpus ID: 116032494

Interior path following primal-dual algorithms

  title={Interior path following primal-dual algorithms},
  author={R. C. Monteiro and I. Adler},
We describe a primal-dual interior point algorithm for linear programming and convex quadratic programming problems which requires a total of O(n$\sp3$L) arithmetic operations. Each iteration updates a penalty parameter and finds an approximate Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithm barrier function problem. The algorithm is based on the path following idea. We show that the duality gap is reduced at each… Expand
Polynomial Convergence of a New Family of Primal-Dual Algorithms for Semidefinite Programming
This paper establishes the polynomial convergence of a new class of primal-dual interior-point path-following feasible algorithms for semidefinite programming (SDP) whose search directions areExpand
A globally convergent primal—dual interior point algorithm for convex programming
  • R. Monteiro
  • Mathematics, Computer Science
  • Math. Program.
  • 1994
This paper studies the global convergence of a large class of primal—dual interior point algorithms for solving the linearly constrained convex programming problem and uses an inexact line search based on Armijo stepsize rule to compute the stepsize. Expand
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  • Y. Ye
  • Mathematics, Computer Science
  • Math. Program.
  • 1991
Neither tracing the central path nor using the projective transformation, the algorithm converges to the optimal solution set in O(\sqrt n L) iterations and uses O(n3L) total arithmetic operations. Expand
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An $$O(\sqrt n L)$$ iteration bound primal-dual cone affine scaling algorithm for linear programmingiteration bound primal-dual cone affine scaling algorithm for linear programming
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Primal-Dual Affine Scaling Interior Point Methods for Linear Complementarity Problems
  • F. Potra
  • Mathematics, Computer Science
  • SIAM J. Optim.
  • 2008
A first order affine scaling method and two $m$th order affine scaling methods for solving monotone linear complementarity problems (LCPs) are presented. All three methods produce iterates in a wideExpand
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Newton-KKT interior-point methods for indefinite quadratic programming
Numerical results on randomly generated problems suggest that the proposed algorithms may be of great practical interest, and global and local quadratic convergence are proved under nondegeneracy assumptions for both algorithms. Expand