This paper presents a practical and efficient method to solve large-scale nonlinear equations. The global convergence of this new trust region algorithm is verified. The algorithm is then used to solve the nonlinear equations arising in an Expanded Lagrangian Function (ELF). Numerical results for the implementation of some large-scale problems indicate that the algorithm is efficient for these ...

This document discusses the concept of an algorithm designed to locate the optimal solution to a problem in a (presumably) very large solution space. The algorithm attempts to locate the optimal solution to the problem by beginning a search at an arbitrary point in the solution space and then searching in the “local” area around the start point to find better solutions. The algorithm completes ...

Partial closure under weak composition, or partial -consistency for short, is essential for tackling fundamental reasoning problems associated with qualitative constraint networks, such as the satisfiability checking problem, and therefore it is crucial to be able to enforce it as fast as possible. To this end, we propose a new algorithm, called PWC, for efficiently enforcing partial -consisten...

Episiotomy is used almost routinely in vaginal deliveries in Sri Lanka and the norm is for it to be performed without anaesthesia. This is due to the popular belief that episiotomy could be performed painlessly without anaesthesia if it is performed at the peak of a contraction when the perineum is at full stretch. This practice is also convenient, since nurses and midwives involved in normal d...

We propose an extension of the Generalized Balanced Academic Curriculum Problem (GBACP), a relevant planning problem arising in many universities. The problem consists of assigning courses to teaching terms and years, satisfying a set of precedence constraints and balancing students’ load among terms. Differently from the original GBACP formulation, in our case, the same course can be assigned ...

We present a trust region method for minimizing a general diierentiable function restricted to an arbitrary closed set. We prove a global convergence theorem. The trust region method deenes diicult subproblems that are solvable in some particular cases. We analyze in detail the case where the domain is an Euclidean ball. For this case we present numerical experiments where we consider diierent ...

The future of biomass energy in the global energy system depends on many major factors, among others on the attitude of society in rural areas to the biomass energy and the renewable energy resources. Biomass energy plays increasing role in rural areas with its contribution to the self sufficiency of people in the countryside. The paper deals with the analysis the opportunities of utilization o...

We provide a simple convergence analysis unified for TR and a new ARC algorithms, which we name ARCq and which is very close in spirit to trust region methods, closer than the original ARC is. We prove global convergence to second order points. We also obtain as a corollary the convergence of the original ARC method. Since one of our aims is to achieve a simple presentation, we sacrifice some g...