Predictor-corrector Interior Point Method Research Articles

Optimal Truss Design by Interior-Point Methods

This article presents a primal-dual predictor-corrector interior-point method for solving quadratically constrained convex optimization problems that arise from truss design problems. We investigate certain special features of the problem, discuss fundamental differences of interior-point methods for linearly and nonlinearly constrained problems, extend Mehrotra's predictor-corrector strategy to nonlinear programs, and establish convergence of a long step method. Numerical experiments on large scale problems illustrate the surprising efficiency of the method.

An efficient predictor-corrector interior point algorithm for security-constrained economic dispatch

This paper deals with the application of an advanced interior point method to the security-constrained economic dispatch (SCED) problems through successive linear programming. The nonlinear SCED problem is linearized, and then solved by a predictor-corrector interior point method. Besides describing the basic algorithm, the paper focuses on several important issues that are critical to its efficient implementation, including the adjustment of barrier parameter, the determination of initial point, and so on. Computational experiments are conducted to evaluate their impact on the performance of the algorithm. Some suggestions, such as using the feasibility condition to adjust the way of computing barrier parameter /spl mu/ and customizing initial point by adopting a relative small threshold, are proposed to reduce the overall iterations required by the algorithm. The computational results on power systems of 236 to 2124 buses have shown that these suggestions are very effective, improving the performance of the algorithm by a factor of 2. Comparison with a pure primal-dual interior point method is also provided to demonstrate the superiority of the proposed predictor-corrector method.

Interior point SQP strategies for structured process optimization problems

Successive Quadratic Programming (SQP) has been the method of choice for the solution of nonlinear programming problems. For the solution of large problems with SQP based codes, the combinatorial complexity associated with active set methods for the treatment of inequalities has been a bottleneck in exploiting the problem structure. In this paper, we examine the merits of incorporating an interior point method within an SQP framework and the significant computational savings are demonstrated on problems drawn from optimal control. We also provide a novel intepretation of the popularly used predictor-corrector interior point method using the principles of reduced Hessian SQP (rSQP).

An implementation of a parallel primal-dual interior point method for block-structured linear programs

An implementation of the primal-dual predictor-corrector interior point method is specialized to solve block-structured linear programs with side constraints. The block structure of the constraint matrix is exploited via parallel computation. The side constraints require the Cholesky factorization of a dense matrix, where a method that exploits parallelism for the dense Cholesky factorization is used. For testing, multicommodity flow problems were used. The resulting implementation is 65%–90% efficient, depending on the problem instance. For a problem with K commodities, an approximate speedup for the interior point method of 0.8K is realized.