An algorithm for solving large nonlinear optimization problems with simple bounds is described. It is based on the gradient projection method and uses a limited-memory BFGS matrix to approximate the Hessian of the objective function. We show how to take advantage of the form of the limited-memory approximation to implement the algorithm eeciently. The results of numerical tests on a set of larg...

A Hessian matrix in full waveform inversion (FWI) is difficult to compute directly because of high computational cost and an especially large memory requirement. Therefore, Newton-like methods are rarely feasible in realistic large-size FWI problems. We modify the quasi-Newton BFGS method to use a projected Hessian matrix that reduces both the computational cost and memory required, thereby mak...

An algorithm for solving large nonlinear optimization problems with simple bounds is described. It is based on the gradient projection method and uses a limited-memory BFGS matrix to approximate the Hessian of the objective function. We show how to take advantage of the form of the limited-memory approximation to implement the algorithm eeciently. The results of numerical tests on a set of larg...

We propose a new framework for black-box convex optimization which is well-suited for situations where gradient computations are expensive. We derive a new method for this framework which leverages several concepts from convex optimization, from standard first-order methods (e.g. gradient descent or quasi-Newton methods) to analytical centers (i.e. minimizers of self-concordant barriers). We de...

Deterministic optimization algorithms, that are combination of direct search methods and local search algorithms, are proposed for molecular conformation problems. We apply these methods to solve the Lennard-Jones atomic cluster problem. The deterministic optimization algorithms are embedded in a build-up scheme. At each stage, an atom is added to an optimized structure of a small cluster, and ...

Evolutionary approaches to molecular docking typically hybridize with local search methods, more specifically, the Solis-Wet method. However, some studies indicated that local search methods might not be very helpful in the context of molecular docking. An evolutionary algorithm with proper genetic operators can perform equally well or even outperform hybrid evolutionary approaches. We show tha...

A photodiode array (PDA) spectrophotometer was used to study the fading reaction of phenolpthalein in dilute sodium hydroxide solution. The principal component analysis (PCA) method was employed to identify the number of light absorbing species in the kinetics system. The target factor analysis (TFA) procedure, coupled with the Broyden-Fletcher-Goldfard-Shanno (BFGS) optimization method, was ap...

Nonlinear optimization problems with dynamical parameters are widely arising in many practical scientific and engineering applications, various computational models presented for solving them under the hypothesis of short-time invariance. To eliminate large lagging error solution inherently dynamic nonlinear problem, only way is to estimate future unknown information by using present previous d...