The traditional bundle adjustment algorithm for structure from motion problem has a computational complexity of O((m + n)) per iteration and memory requirement of O(mn(m+n)), where m is the number of cameras and n is the number of structure points. The sparse version of bundle adjustment has a computational complexity of O(m+mn) per iteration and memory requirement of O(mn). Here we propose an ...

We consider the infinite-horizon discounted optimal control problem formalized by Markov Decision Processes. We focus on Policy Search algorithms, that compute an approximately optimal policy by following the standard Policy Iteration (PI) scheme via an -approximate greedy operator (Kakade and Langford, 2002; Lazaric et al., 2010). We describe existing and a few new performance bounds for Direc...

There is too much iteration when using the traditional Floyd algorithm to calculate the shortest path, that is to say, the computation of traditional Floyd algorithm is too large for an urban road network with a large number of nodes. As for this disadvantage, the Floyd algorithm was improved and optimized further in this study; moreover, the improved Floyd algorithm was used to solve the short...

We introduce in this paper an optimal first-order method that allows an easy and cheap evaluation of the local Lipschitz constant of the objective’s gradient. This constant must ideally be chosen at every iteration as small as possible, while serving in an indispensable upper bound for the value of the objective function. In the previously existing variants of optimal first-order methods, this ...

We develop the Sparse Approximate Matrix Multiply (SpAMM) n-body solver for first order Newton Schulz iteration of the matrix square root and inverse square root. The solver performs recursive two-sided metric queries on a modified Cauchy-Schwarz criterion (octree-occlusion-culling in the ijkcube), yielding a bounded relative error in the matrix-matrix product and reduced complexity for problem...

In this paper, we present a convergence rate analysis for the inexact Krasnosel’skĭı– Mann iteration built from nonexpansive operators. Our results include two main parts: we first establish global pointwise and ergodic iteration–complexity bounds, and then, under a metric subregularity assumption, we establish local linear convergence for the distance of the iterates to the set of fixed points...

This paper establishes the polynomial iteration-complexity bounds of the well known algorithms for linear programming, namely the shortstep path-following algorithm of Kojima et al., carry over to the context of SDLCP. Mathematics Subject Classification: 90C33, 65G20, 65G50

It is shown that, unless P NP, local search algorithms for the traveling salesman problem having polynomial time complexity per iteration will generate solutions arbitrarily far from the optimal.

We introduce a new formulation for total variation minimisation in image denoising. We also present a linearly convergent first-order method for solving this reformulated problem and show that it possesses a nearly dimension-independent iteration complexity bound.