In this paper, we solve unconstrained optimization problem using a free line search steepest descent method. First, we propose a double parameter scaled quasi Newton formula for calculating an approximation of the Hessian matrix. The approximation obtained from this formula is a positive definite matrix that is satisfied in the standard secant relation. We also show that the largest eigen value...

The minimization problem of an L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints is formulated for a class of two-dimensional (2-D) state-space digital filters. First, the problem is converted into an unconstrained optimization problem by using linear-algebraic techniques. Next, the unconstrained optimization problem is solved by applying an efficient quasi-Newton algo...

The problem of minimizing an L2-sensitivity measure subject to L2norm dynamic-range scaling constraints for state-space digital filters is formulated. It is shown that the problem can be converted into an unconstrained optimization problem by using linear-algebraic techniques. Next, the unconstrained optimization problem is solved by applying an efficient quasi-Newton algorithm with closed-form...

This paper investigates the minimization problem of weighted roundoff noise and pole sensitivity subject to l2-scaling constraints for state-space digital filters. A new measure for evaluating roundoff noise and pole sensitivity is proposed, and an efficient technique for minimizing this measure is developed. It is shown that the problem can be converted into an unconstrained optimization probl...

In this article, adaptive resource allocation (ARA) is investigated for multiple primary networks based-cognitive radio networks under a more practical system model, where the bandwidth of each secondary user is assumed to be limited and the maximum allowable interference for each primary network is different. We first formulate the ARA as a constrained optimization problem with the objective f...

In [1] (Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization J. Optimization. Theory Appl. 141 (2009) 249 - 264), an efficient hybrid conjugate gradient algorithm, the CCOMB algorithm is proposed for solving unconstrained optimization problems. However, the proof of Theorem 2.1 in [1] is incorrect due to an erroneous inequality which used to indicate the descent property for the s...

A new approach to the problem of minimizing L2sensitivity subject to L2-norm scaling constraints for two-dimensional (2-D) state-space digital filters is proposed. Using linear-algebraic techniques, the problem at hand is converted into an unconstrained optimization problem, and the unconstrained problem obtained is then solved by applying an efficient quasi-Newton algorithm. Computer simulatio...

In this paper we examine a technique by which fault tolerance can be embedded into a feedforward network leading to a network tolerant to the loss of a node and its associated weights. The fault tolerance problem for a feedforward network is formulated as a constrained minimax optimization problem. Two different methods are used to solve it. In the first method, the constrained minimax optimiza...