In this note we consider a large step modiication of the Mizuno-Todd-Ye O(p nL) predictor-corrector interior-point algorithm for linear programming. We demonstrate that the modiied algorithm maintains its O(p nL)-iteration complexity, while exhibiting superlinear convergence for general problems and quadratic convergence for non-degenerate problems. To our knowledge, this is the rst constructio...

We propose and study the iteration-complexity of a proximal-Newton method for finding approximate solutions of the problem of minimizing a twice continuously differentiable convex function on a (possibly infinite dimensional) Hilbert space. We prove global convergence rates for obtaining approximate solutions in terms of function/gradient values. Our main results follow from an iteration-comple...

We present a new corrector-predictor method for solving sufficient linear complementarity problems for which a sufficiently centered feasible starting point is available. In contrast with its predictor-corrector counterpart proposed by Miao, the method does not depend on the handicap κ of the problem. The method has O((1+ κ)√nL)-iteration complexity, the same as Miao’s method, but our error est...

Different processors work with disparate speeds. For any given processor, elementary operations differ in terms of their speeds and computational complexities. The paper presents an algorithm to compute cubes of 1st "N" Natural Numbers using one multiplication by constant, two additions on variables and one addition by constant, per iteration. Theoretically, computational complexity o...

A predictor-corrector method for solving the P (k)-matrix linear complementarity problems from infeasible starting points is analyzed. Two matrix factorizations and at most three backsolves are to be computed at each iteration. The computational complexity depends on the quality of the starting points. If the starting points are large enough then the algorithm has O ? (+ 1) 2 nL iteration compl...

We propose and analyse primal-dual interior-point algorithms for convex optimization problems in conic form. The families of algorithms whose iteration complexity we analyse are so-called short-step algorithms. Our iteration complexity bounds match the current best iteration complexity bounds for primal-dual symmetric interior-point algorithm of Nesterov and Todd, for symmetric cone programming...

Pointwise and ergodic iteration-complexity results for the proximal alternating direction method of multipliers (ADMM) for any stepsize in (0, (1 + √ 5)/2) have been recently established in the literature. In addition to giving alternative proofs of these results, this paper also extends the ergodic iteration-complexity result to include the case in which the stepsize is equal to (1+ √ 5)/2. As...

In this paper we propose new primal-dual interior point methods (IPMs) for P∗(κ) linear complementarity problems (LCPs) and analyze the iteration complexity of the algorithm. New search directions and proximity measures are defined based on a class of kernel functions, ψ(t) = t 2−1 2 − R t 1 e q “ 1 ξ −1 ” dξ, q ≥ 1. If a strictly feasible starting point is available and the parameter q = log „...

Newton iteration is known (under some precise conditions) to converge quadratically to zeros of non-degenerate systems of polynomials. This and other properties may be used to obtain theorems on the global complexity of solving systems of polynomial equations (See Shub and Smale in [6]), using a model of computability over the reals. However, it is not practical (and not desirable) to actually ...

Newton iteration is known (under some precise conditions) to converge quadratically to zeros of non-degenerate systems of polynomials. This and other properties may be used to obtain theorems on the global complexity of solving systems of polynomial equations (See Shub and Smale in 6]), using a model of computability over the reals. However, it is not practical (and not desirable) to actually c...