We investigate the behavior of quasi-Newton algorithms applied to minimize a nonsmooth function f , not necessarily convex. We introduce an inexact line search that generates a sequence of nested intervals containing a set of points of nonzero measure that satisfy the Armijo and Wolfe conditions if f is absolutely continuous along the line. Furthermore, the line search is guaranteed to terminat...

We give a pattern search method for nonlinearly constrained optimization that is an adaption of a bound constrained augmented Lagrangian method first proposed by Conn, Gould, and Toint [SIAM J. Numer. Anal., 28 (1991), pp. 545–572]. In the pattern search adaptation, we solve the bound constrained subproblem approximately using a pattern search method. The stopping criterion proposed by Conn, Go...

We propose a family of directions that generalizes many directions proposed so far in interiorpoint methods for the SDP (semide nite programming) and for the monotone SDLCP (semide nite linear complementarity problem). We derive the family from the Helmberg-Rendl-Vanderbei-Wolkowicz/KojimaShindoh-Hara/Monteiro direction by relaxing its \centrality equation" into a \centrality inequality." Using...

Online learning algorithms like the perceptron are widely used for structured prediction tasks. For sequential search problems, like left-to-right tagging and parsing, beam search has been successfully combined with perceptron variants that accommodate search errors (Collins and Roark, 2004; Huang et al., 2012). However, perceptron training with inexact search is less studied for bottom-up pars...

Many optimization algorithms require gradients of the model functions, but computing accurate gradients can be computationally expensive. We study the implications of using inexact gradients in the context of the multilevel optimization algorithm MG/Opt. MG/Opt recursively uses (typically cheaper) coarse models to obtain search directions for finer-level models. However, MG/Opt requires the gra...

-This paper describes a framework for performing relational graph matching using genetic search. There are three novel ingredients to the work. Firstly, we cast the optimisation process into a Bayesian framework by exploiting the recently reported global consistency measure of Wilson and Hancock as a fitness measure. The second novel idea is to realise the crossover process at the level of subg...

Based on the secant condition often satisfied by quasi-Newton methods, two new versions of the Hestenes-Stiefel (HS) nonlinear conjugate gradient method are proposed, which are descent methods even with inexact line searches. The search directions of the proposed methods have the form dk = −θk gk + β H S k dk−1, or dk = −gk + β H S k dk−1 + θk yk−1. When exact line searches are used, the propos...

In this paper we propose an appealing inexact proximal alternating directions method (abbreviated as In-PADM) for solving a class of monotone variational inequalities with certain special structure, and this structure under consideration is common in practice. We prove convergence of In-PADM method while the inexact term is arbitrary but satisfied some suitable conditions. For solving the varia...

A filter algorithm with inexact line search is proposed for solving nonlinear programming problems. The filter is constructed by employing the norm of the gradient of the Lagrangian function to the infeasibility measure. Transition to superlinear local convergence is showed for the proposed filter algorithm without second-order correction. Under mild conditions, the global convergence can also ...