The Holy Quran was descended from Almighty Allah to the Holy Prophet (AS) about the last 14 centuries and there has been a time interval between descent of the Quran and its existing readers and commentators. This Question is posed whether this time interval between descent of the Quran and commentator will effect on verses understanding and their commentary or not? As one of commentary princip...

Two new nonlinear spectral conjugate gradient methods for solving unconstrained optimization problems are proposed. One is based on the Hestenes and Stiefel (HS) method and the spectral conjugate gradient method. The other is based on a mixed spectral HS-CD conjugate gradient method, which combines the advantages of the spectral conjugate gradient method, the HS method, and the CD method. The d...

In this paper we prove that the broad class of direct-search methods of directional type based on imposing sufficient decrease to accept new iterates shares the worst case complexity bound of steepest descent for the unconstrained minimization of a smooth function, more precisely that the number of iterations needed to reduce the norm of the gradient of the objective function below a certain th...

Based on an eigenvalue analysis, a new proof for the sufficient descent property of the modified Polak-Ribière-Polyak conjugate gradient method proposed by Yu et al. is presented.

In this paper we investigate effective descent morphisms in categories of reflexive and transitive lax algebras. We show in particular that open and proper maps are effective descent, result that extends the corresponding results for the category of topological spaces and continuous maps. Introduction A morphism p : E → B in a category C with pullbacks is called effective descent if it allows a...

Overseas investigations have shown that many healthcare institutions are understocked of antidotes to treat these patients. 1–4 Despite a recent study to the contrary, 5 the paper by Fountain and colleagues, published in this issue of the New Zealand Medical Journal, suggests similar problems in New Zealand hospitals with shortcomings in hospital pharmacy stocks and resupply. 6 The paper raises...

We study the problem of estimating parameters a Boolean product distribution in d dimensions, when samples are truncated by set $$S \subseteq \{0, 1\}^d$$ accessible through membership oracle. This is first time that computational and statistical complexity learning from considered discrete setting. introduce natural notion fatness truncation S, under which reveal enough information about true ...

We propose and analyze a randomized zeroth-order optimization method based on approximating the exact gradient by finite differences computed in set of orthogonal random directions that changes with each iteration. A number previously proposed methods are recovered as special cases including spherical smoothing, coordinate descent, well discretized descent. Our main contribution is proving conv...

This paper studies the relations between the local minima of a cost function f and the stable equilibria of the gradient descent flow of f . In particular, it is shown that, under the assumption that f is real analytic, local minimality is necessary and sufficient for stability. Under the weaker assumption that f is indefinitely continuously differentiable, local minimality is neither necessary...