A q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems

A Polak–Ribière–Polyak (PRP) algorithm is one of the oldest and popular conjugate gradient algorithms for solving nonlinear unconstrained optimization problems. In this paper, we present a q-variant of the PRP (q-PRP) method for which both the sufficient and conjugacy conditions are satisfied at every iteration. The proposed method is convergent globally with standard Wolfe conditions and strong Wolfe conditions. The numerical results show that the proposed method is promising for a set of given test problems with different starting points. Moreover, the method reduces to the classical PRP method as the parameter q approaches 1.

A New conjugate gradient method for unconstrained optimization problems with descent property

In this paper, we propose a new conjugate gradient method for solving nonlinear unconstrained optimization. The new method consists of three parts, the first part of them is the parameter of Hestenes-Stiefel (HS). The proposed method is satisfying the descent condition, sufficient descent condition and conjugacy condition. We give some numerical results to show the efficiency of the suggested method.

A COMPARATIVE STUDY OF SOME MODIFICATIONS OF CG METHODS UNDER EXACT LINE SEARCH

Conjugate Gradient (CG) method is a technique used in solving nonlinear unconstrained optimization problems. In this paper, we analysed the performance of two modifications and compared the results with the classical conjugate gradient methods of. These proposed methods possesse global convergence properties for general functions using exact line search. Numerical experiments show that the two modifications are more efficient for the test problems compared to classical CG coefficients.

Non-recombining trinomial tree pricing model and calibration for the volatility smile

In this paper, we consider the non-recombining trinomial tree pricing model under the volatility, which is a function of time, establish the option pricing model and give the convergence rates of the non-recombining trinomial tree method. In addition, we research the calibration problem of volatility and adopt an exterior penalty method to transform this problem into a nonlinear unconstrained optimization problem. For the optimization problem, we use the quasi-Newton algorithm. Finally, we test our model by numerical examples and options data on the S&P 500 index. The results show the effectiveness of the non-recombining trinomial tree pricing model.

A New Hybrid Algorithm for Convex Nonlinear Unconstrained Optimization

In this study, we tend to propose a replacement hybrid algorithmic rule which mixes the search directions like Steepest Descent (SD) and Quasi-Newton (QN). First, we tend to develop a replacement search direction for combined conjugate gradient (CG) and QN strategies. Second, we tend to depict a replacement positive CG methodology that possesses the adequate descent property with sturdy Wolfe line search. We tend to conjointly prove a replacement theorem to make sure global convergence property is underneath some given conditions. Our numerical results show that the new algorithmic rule is powerful as compared to different standard high scale CG strategies.

On Laterally Perturbed Human Stance: Experiment, Model, and Control

Understanding human balance is a key issue in many research areas. One goal is to suggest analytical models for the human balance. Specifically, we are interested in the stability of a subject when a lateral perturbation is being applied. Therefore, we conducted an experiment, laterally perturbing five subjects on a mobile platform. We observed that the recorded motion is divided into two parts. The legs act together as a first, the head-arms-trunk segment as a second rigid body with pelvis, and the ankle as hinge joints. Hence, we suggest using a planar double-inverted pendulum model for the analysis. We try to reproduce the human reaction utilizing torque control, applied at the ankle and pelvis. The fitting was realized by least square and nonlinear unconstrained optimization on training sets. Our model is not only able to fit to the human reaction, but also to predict it on test sets. We were able to extract and review key features of balance, like torque coupling and delays as outcomes of the aforementioned optimization process. Furthermore, the delays are well within the ranges typically for such compensatory motions, composed of reflex and higher level motor control.