Recent work has shown that stochastically perturbed gradient methods can efficiently escape strict saddle points of smooth functions. We extend this body to nonsmooth optimization, by analyzing an inexact analogue a method applied the Moreau envelope. The main conclusion is variety algorithms for optimization envelope at controlled rate. technical insight many proximal subproblem yield directio...

We investigate the BFGS algorithm with an inexact line search when applied to nonsmooth functions, not necessarily convex. We define a suitable line search and show that it generates a sequence of nested intervals containing points satisfying the Armijo and weak Wolfe conditions, assuming only absolute continuity. We also prove that the line search terminates for all semi-algebraic functions. T...

This tutorial describes the classic method of conjugate directions: the generalization of the conjugate-gradient method in iterative least-square inversion. I derive the algebraic equations of the conjugate-direction method from general optimization principles. The derivation explains the “magic” properties of conjugate gradients. It also justifies the use of conjugate directions in cases when ...

Conjugate gradient methods are a class of important methods for unconstrained optimization, especially when the dimension is large. This paper proposes a new conjugacy condition, which considers an inexact line search scheme but reduces to the old one if the line search is exact. Based on the new conjugacy condition, two nonlinear conjugate gradient methods are constructed. Convergence analysis...

Search Computing (SeCo) is a project funded by the European Research Council (ERC). It focuses on building the answers to complex search queries like “Where can I attend an interesting conference in my field close to a sunny beach?” by interacting with a constellation of cooperating search services, using ranking and joining of results as the dominant factors for service composition. SeCo start...

This paper proposes an image retrieval model for in dexing and retrieving images with fuzzy triples. Th e well known triple framework based on 2 dimensional (2D) strings is a novel index mechanism in that it allows us to simply specify the spatial structure o f images, guaranteeing fast retrieval time. However , there are two significant drawbacks in this framewo rk; one is that it can not acco...

In this paper, a fast algorithm is proposed for block motion estimation for video sequences. The proposed algorithm is proven to be equivalent to exhaustive search. In a multiresolution approach, it uses mathematically derived threshold to prune search candidates whose low-resolution versions are too far from the low resolution version of the block for which a best match is sought. Experimental...