Sharif Digital Repository

We have recently proposed a structured algorithm for solving constrained nonlinear least-squares problems and established its local two-step Q-superlinear convergence rate. The approach is based on an earlier adaptive structured scheme due to Mahdavi-Amiri and Bartels of the exact penalty method. The structured adaptation makes use of the ideas of Nocedal and Overton for handling quasi-Newton updates of projected Hessians and adapts a structuring scheme due to Engels and Martinez. For robustness, we have employed a specific nonsmooth line search strategy, taking account of the least-squares objective. Numerical results also confirm the practical relevance of our special considerations for... 

Based on two modified secant equations proposed by Yuan, and Li and Fukushima, we extend the approach proposed by Andrei, and introduce two hybrid conjugate gradient methods for unconstrained optimization problems. Our methods are hybridizations of Hestenes-Stiefel and Dai-Yuan conjugate gradient methods. Under proper conditions, we show that one of the proposed algorithms is globally convergent for uniformly convex functions and the other is globally convergent for general functions. To enhance the performance of the line search procedure, we propose a new approach for computing the initial value of the steplength for initiating the line search procedure. We give a comparison of the... 

In this paper, we propose a new trust-region method for solving nonlinear systems of equalities and inequalities. The algorithm combines both standard and adaptive trust-region frameworks to construct the steps of the algorithm. The trust-region subproblem is solved in the first iteration using a given initial radius. Then, in each iteration, the standard trust-region method is followed whenever the current trial step is accepted, otherwise, the subproblem is resolved using an adaptive scheme. The convergence results for the new proposed algorithm are established under some mild and standard assumptions. Numerical results on some least-squares test problems show the efficiency and... 

We propose a modified structured secant relation to get a more accurate approximation of the second curvature of the least squares objective function. Then, using this relation and an approach introduced by Andrei, we propose three scaled nonlinear conjugate gradient methods for nonlinear least squares problems. An attractive feature of one of the proposed methods is satisfication of the sufficient descent condition regardless of the line search and the objective function convexity. We establish that the three proposed algorithms are globally convergent, under the assumption of the Jacobian matrix having full column rank on the level set for one, and without such assumption for the other... 

We propose a modified structured secant relation to get a more accurate approximation of the second curvature of the least squares objective function. Then, using this relation and an approach introduced by Andrei, we propose three scaled nonlinear conjugate gradient methods for nonlinear least squares problems. An attractive feature of one of the proposed methods is satisfication of the sufficient descent condition regardless of the line search and the objective function convexity. We establish that the three proposed algorithms are globally convergent, under the assumption of the Jacobian matrix having full column rank on the level set for one, and without such assumption for the other... 

We present a high-performance and efficiently simplified new neural network which improves the existing neural networks for solving general linear and quadratic programming problems. The network, having no need for parameter setting, results in a simple hardware requiring no analog multipliers, is shown to be stable and converges globally to the exact solution. Moreover, using this network we can solve both linear and quadratic programming problems and their duals simultaneously. High accuracy of the obtained solutions and low cost of implementation are among the features of this network. We prove the global convergence of the network analytically and verify the results numerically. © 2005... 

Following the approach proposed by Dai and Liao, we introduce two nonlinear conjugate gradient methods for unconstrained optimization problems. One of our proposed methods is based on a modified version of the secant equation proposed by Zhang, Deng and Chen, and Zhang and Xu, and the other is based on the modified BFGS update proposed by Yuan. An interesting feature of our methods is their account of both the gradient and function values. Under proper conditions, we show that one of the proposed methods is globally convergent for general functions and that the other is globally convergent for uniformly convex functions. To enhance the performance of the line search procedure, we also... 

The presence of bias in measurement of rate gyros is a performance limiting factor for satellite attitude determination systems. Gyro bias is usually handled by Kalman filtering methods which are mostly based on linearization approaches and lack global convergence properties. On the other hand, the existing asymptotically convergent nonlinear observers take into account the gyro bias only when multiple vector measurements are available. We present an asymptotically convergent attitude estimator which uses only one vector measurement and a rate gyro whose output is contaminated with an unknown and constant bias. The effect of unknown bias is compensated by means of a parameter adaptation law.... 

We present a method for global estimation of joint velocities in rigid manipulators. A class of velocity observers with smooth dynamics are introduced whose structure depend on freely selectable functions and gains giving the flexibility of achieving multiple design objectives at the same time. Unlike most methods, no a priori knowledge of an upper bound for velocity magnitude is used. An adaptive version of the observer is also presented to handle a class of structured uncertainties in manipulator model. Simulation example illustrates low noise sensitivity of the globally convergent observer in comparison with semi-globally convergent observers. © 2009 IEEE