The limiting behavior of weighted paths associated with the semidefinite program (SDP) map $X^{1/2}SX^{1/2}$ was studied and some applications to error bound analysis and superlinear convergence of a class of
primal-dual interior-point methods were provided. A new approach for solving large-scale well-structured sparse SDPs via a saddle point mirror-prox algorithm with ${cal O}(epsilon^{-1})$ efficiency was developed based on exploiting sparsity structure and reformulating SDPs into smooth convex-concave saddle point problems. An iterative solver-based
long-step primal-dual infeasible path-following algorithm for convex quadratic programming (CQP) was developed. The search directions of
this algorithm were computed by means of a preconditioned iterative linear solver. A uniform bound, depending only on the CQP data, on
the number of iterations performed by a preconditioned iterative linear solver was established. A polynomial bound on the number of
iterations of this algorithm was also obtained. One efficient ``nearly exact' type of method for solving large-scale ``low-rank' trust region
subproblems was proposed by completely avoiding the computations of Cholesky or partial Cholesky factorizations. A computational study of this method was also provided by applying it to solve some large-scale nonlinear programming problems.
| Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/7151 |
| Date | 24 June 2005 |
| Creators | Lu, Zhaosong |
| Publisher | Georgia Institute of Technology |
| Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
| Format | 774541 bytes, application/pdf |
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