Domains in Continuous Constraint Programming (CP) are generally represented with intervals whose n-ary Cartesian product (box) approximates the solution space. This paper proposes a new representation for continuous variable domains based on octagons. We generalize local consistency and split to this octagon representation, and we propose an octagonal-based branch and prune algorithm. Prelimina...

A numerical algorithm is proposed for computing an extreme eigenpair of a symmetric/positive-definite matrix pencil (A, B). The leftmost or the rightmost eigenvalue can be targeted. Knowledge of (A, B) is only required through a routine that performs matrix-vector products. The method has excellent global convergence properties and its local rate of convergence is superlinear. It is based on a ...

k is a continuously differentiable function, bounded from below, two main approaches are operational to date. The first one is based on the line-search concept which assures the global convergence of the methods. The idea is to use a quadratic model in order to generate a search direction and then find a suitable stepsize along the direction. Although it is successful at most time it does not u...

A line-search method, based on retractions, is formulated on Riemannian manifolds. This Riemannian line-search method, as well as a previouslyproposed Riemannian trust-region method, are further generalized to accelerated line-search and trust-region methods, where the next iterate is allowed to be any point that produces at least as much decrease in the cost function as a fixed fraction of the...

A multivariate analysis of inadequate extradural analgesia was carried out prospectively on 1051 patients undergoing lumbar extradural anaesthesia for surgery performed on structures innervated by T10-S5. Ninety-six patients (9%) experienced pain during surgery. Age, extradural fentanyl, diazepam sedation and duration of surgery had no significant influence. We found some weak evidence that the...

We present in this paper a class of trust region algorithms in which the structure of the problem is explicitly used in the very denition of the trust region itself. This development is intended to re BLOCKINect the possibility that some parts of the problem may be more \trusted" than others, a commonly occurring situation in large-scale nonlinear applications. After describing the structured t...

Stimulated small-angle light scattering was used to measure the structure factor of a Bose-Einstein condensate in the phonon regime. The excitation strength for phonons was found to be significantly reduced from that of free particles, revealing the presence of correlated pair excitations and quantum depletion in the condensate. The Bragg resonance line strength and line shift agreed with predi...

BACKGROUND Inguinal hernia surgery has undergone numerous advances in the last few years. This study analysed the changes in the practice of one surgeon in a district general hospital over a seven year interval. The effect of changing from Bassini to Lichtenstein repair in 1994 was evaluated. METHODS The study involved two parts: first a search of a computerised database of inguinal hernia pr...

Primary hyperhidrosis commonly affects the axillae, palms, soles, scalp, face, and groin. Patients may have multiple areas involved making localized therapy challenging. Systemic therapy may be necessary and can be used as monotherapy or combined with other hyperhidrosis treatments for optimal outcomes. Systemic therapy can also be used to treat secondary hyperhidrosis and compensatory hyperhid...

This paper presents a Riemannian trust region algorithm for unconstrained optimization problems with locally Lipschitz objective functions defined on complete Riemannian manifolds. To this end we define a function Φ : TM → R on the tangent bundle TM , and at k-th iteration, using the restricted function Φ|TxkM where TxkM is the tangent space at xk, a local model function Qk that carries both fi...