We consider the problem of minimizing a high-dimensional objective function, which may include regularization term, using only (possibly noisy) evaluations function. Such optimization is also called derivative-free, zeroth-order, or black-box optimization. propose new zeroth-order regularized method, dubbed ZORO. When underlying gradient approximately sparse at an iterate, ZORO needs very few f...

It is well known that the chemical behavior of a compound is dependent upon the structure of itsmolecules. Quantitative structure – activity relationship (QSAR) studies and quantitative structure –property relationship (QSPR) studies are active areas of chemical research that focus on the nature ofthis dependency. Topological indices are the numerical value associated with chemical constitution...

Bessel beams (BBs) have gained prominence thanks to their diffraction-free propagation and self-healing properties. These are conventionally generated using different approaches, namely by transforming a narrow circular beam with lens, axicons or holographic beam-shaping techniques. methods involve space-consuming optics. To overcome this limitation, in the past, efforts been made create BBs di...

In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems. We establish the complexity of this method for computing an approximate stationary point of a nonlinear programming problem. We also show that this method pos...

based on the randic suggestion of the resolution of a structure into shape, size, and function an index representing structure-catabolic fate relationships of amino acids is constructed. the index obtained by multiplying three factors; (nb2 + nr), nc and m; representing shape, size and function respectively, where nb2 = number of double bonds, nr = number of rings, nc = number of carbon atoms, ...

in this paper, a new molecular-structure descriptor, the general sum–connectivity co–index  is considered, which generalizes the first zagreb co–index and the general sum–connectivity index of graph theory. we mainly explore the lower and upper bounds in termsof the order and size for this new invariant. additionally, the nordhaus–gaddum–type resultis also represented.