More than a decade agao, Newton’s method has been proposed for constructing the convex best interpolant. Its local quadratic convergence has only been established recently by recasting it as the generalized Newton method for semismooth equations. It still remains mysterious that the Newton method coupled with line search strategies works practically well in global sense. Similar to the classica...

Backtracking search algorithm is a novel population-based stochastic technique. This paper proposes an improved backtracking search algorithm for constrained optimization problems. The proposed algorithm is combined with differential evolution algorithm and the breeder genetic algorithm mutation operator. The differential evolution algorithm is used to accelerate convergence at later iteration ...

In this dissertation we investigate theoretical aspects of some practical approaches used in solving and understanding search problems. We concentrate on the Satisfiability problem, which is a strong representative from search problem domains. The work develops general theoretical foundations to investigate some practical aspects of satisfiability search. This results in a better understanding ...

There has been much recent interest in finding unconstrained local minima of smooth functions, due in part of the prevalence of such problems in machine learning and robust statistics. A particular focus is algorithms with good complexity guarantees. Second-order Newton-type methods that make use of regularization and trust regions have been analyzed from such a perspective. More recent proposa...

This paper addresses the following question: what is the essential difference between stochastic local search (LS) and systematic backtracking (BT) that gives LS superior scalability? One possibility is LS’s lack of firm commitment to any variable assignment. Three BT algorithms are modified to have this feature by introducing randomness into the choice of backtracking variable: a forward check...

In this paper, we describe a new active-set algorithmic framework for minimizing a function over the simplex. The method is quite general and encompasses different active-set Frank-Wolfe variants. In particular, we analyze convergence (when using Armijo line search in the calculation of the stepsize) for the active-set versions of standard Frank-Wolfe, away-step Frank-Wolfe and pairwise Frank-W...

A distributed concurrent search algorithm for distributed constraint satisfaction problems (DisCSPs) is presented. Concurrent search algorithms are composed of multiple search processes (SPs) that operate concurrently and scan non-intersecting parts of the global search space. Each SP is represented by a unique data structure, containing a current partial assignment (CPA), that is circulated am...

This paper extends Escardó and Oliva’s selection monad to the selection monad transformer, a general monadic framework for expressing backtracking search algorithms in Haskell. The use of the closely related continuation monad transformer for similar purposes is also discussed, including an implementation of a DPLL-like SAT solver with no explicit recursion. Continuing a line of work exploring ...

The least squares adjustment (LSA) method is studied as an optimisation problem and shown to be equivalent to the undamped Gauss-Newton (GN) optimisation method. Three problem-independent damping modifications of the GN method are presented: the line-search method of Armijo (GNA); the LevenbergMarquardt algorithm (LM); and Levenberg-Marquardt with Powell dogleg (LMP). Furthermore, an additional...

We propose a novel adaptive damping algorithm for the self-consistent field (SCF) iterations of Kohn-Sham density-functional theory, using backtracking line search to automatically adjust in each SCF step. This is based on theoretically sound, accurate and inexpensive model energy as function parameter. In contrast usual damped schemes, resulting fully automatic does not require user select dam...