This paper considers the fixed point problem for a nonexpansive mapping on a real Hilbert space and proposes novel line search fixed point algorithms to accelerate the search. The termination conditions for the line search are based on the well-known Wolfe conditions that are used to ensure the convergence and stability of unconstrained optimization algorithms. The directions to search for fixe...

Robotic motion planning problems are typically solved by constructing a search tree of valid maneuvers from a start to a goal configuration. Limited onboard computation and real-time planning constraints impose a limit on how large this search tree can grow. Heuristics play a crucial role in such situations by guiding the search towards potentially good directions and consequently minimizing se...

This paper proposes a generalized descent directions-guided multiobjective algorithm (DDMOA2). DDMOA2 uses the scalarizing fitness assignment in its parent and environmental selection procedures. The population consists of leader and non-leader individuals. Each individual in the population is represented by a tuple containing its genotype as well as the set of strategy parameters. The main nov...

We propose a new truncated Newton method for large scale unconstrained optimization, where a Conjugate Gradient (CG)-based technique is adopted to solve Newton’s equation. In the current iteration, the Krylov method computes a pair of search directions: the first approximates the Newton step of the quadratic convex model, while the second is a suitable negative curvature direction. A test based...

In this work, a new search procedure for statistical machine translation (SMT) is proposed that is based on dynamic programming (DP). The starting point is a DP solution to the traveling salesman problem that works by jointly processing tours that visit the same subset of cities. For SMT, the cities correspond to source sentence positions to be translated. Imposing restrictions on the order in ...

This paper establishes the polynomialconvergence of the class of primal-dualfeasible interior-point algorithms for semideenite programming (SDP) based on Monteiro and Zhang family of search directions. In contrast to Monteiro and Zhang's work, no condition is imposed on the scaling matrix that determines the search direction. We show that the polynomial iteration-complexity bounds of two well-k...

This paper presents sequential and parallel derivative-free algorithms for finding a local minimum of smooth and nonsmooth functions of practical interest. It is proved that, under mild assumptions, a sufficient decrease condition holds for a nonsmooth function. Based on this property, the algorithms explore a set of search directions and move to a point with a sufficiently lower functional val...

We propose a new truncated Newton method for large scale unconstrained optimization, where a Conjugate Gradient (CG)-based technique is adopted to solve Newton’s equation. In the current iteration, the Krylov method computes a pair of search directions: the first approximates the Newton step of the quadratic convex model, while the second is a suitable negative curvature direction. A test based...

As the number of documents on the web has proliferated, the low precision of conventional web search engines and the flat ranked search results presentation make it difficult for users to locate specific information of interest. Grouping web search results into a hierarchy of topics provides an alternative to the flat ranked list and facilitates searching and browsing. In this paper, we present...

We consider the problem of minimizing a continuous function that may be nonsmooth and nonconvex, subject to bound constraints. We propose an algorithm that uses the L-BFGS quasi-Newton approximation of the problem’s curvature together with a variant of the weak Wolfe line search. The key ingredient of the method is an active-set selection strategy that defines the subspace in which search direc...