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In this paper we present a new iteration-complexity bound for the Mizuno--Todd--Ye predictor-corrector (MTY P-C) primal-dual interior-point algorithm for linear programming. The analysis of the paper is based on the important notion of crossover events introduced by Vavasis and Ye. For a standard form linear program min {cTχ: Aχ = b, &chi ≥ 0 } with decision variable ..., we show that the MTY P-C algorithm, started from a well-centered interior-feasible solution with duality gap nμ0 finds an interior-feasible solution with duality gap less than nn in O (T(μ0/η)+n3.5 log (Χ*A)) iterations, where T(t ) =min {n² log (log t), log t} for all t>0 and Χ*A is a scaling invariant condition number associated with the matrix A. More specifically,Χ*A is the infimum of all the conditions numbers XAD, where D varies over the set of positive diagonal matrices. Under the setting of the Turing machine model, our analysis yields an O (n3.5 LA + min {n² log L, L}) iteration-complexity bound for the MTY P-C algorithm to find a primal-dual optimal solution, where LA and L are the input sizes of the matrix A and the data (A,b,c ), respectively. This contrasts well with the classical iteration-complexity bound for the MTY P-C algorithm, which depends linearly on L instead of log L. [ABSTRACT FROM AUTHOR]

Models for long-term planning often lead to infinite-horizon stochastic programs that offer significant challenges for computation. Finite-horizon approximations are often used in these cases, but they may also become computationally difficult. In this paper, we directly solve for value functions of infinite-horizon stochastic programs. We show that a successive linear approximation method converges to an optimal value function for the case with convex objective, linear dynamics, and feasible continuation. [ABSTRACT FROM AUTHOR]

We present convergence conditions for a generic primal-dual interior-point algorithm with multiple corrector directions. The corrector directions can be generated by any approach. The search direction is obtained by combining predictor and corrector directions through a small linear program. We also propose a new approach to generate corrector directions. This approach generates directions using information from an appropriately defined Krylov subspace. We propose efficient implementation strategies for our approach that follow the analysis of this paper. Numerical experiments illustrating the features of the proposed approach and its practical usefulness are reported. [ABSTRACT FROM AUTHOR]