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...

<span><span>Quasi-Newton methods are a class of numerical for </span>solving the problem unconstrained optimization. To improve overall efficiency resulting algorithms, we use quasi-Newton which is interesting equation. In this manuscript, present modified BFGS update formula based on new equation, give search direction solving optimizations proplems. We analyse convergence ra...

{ We describe a Newton method applied to the evaluation of a critical point of a total energy associated to a shape optimization problem. The key point of these methods is the Hessian of the shape functional. We give an expression of the Hessian as well as the relation with the second-order Eulerian semi-derivative. An application to the electromagnetic shaping of liquid metals process is studi...

In this paper, we propose a general smoothing Broyden-like quasi-Newton method for solving a class of nonsmooth equations. Under appropriate conditions, the proposed method converges to a solution of the equation globally and superlinearly. In particular, the proposed method provides the possibility of developing a quasi-Newton method that enjoys superlinear convergence even if strict complemen...

We present a new matrix-free method for the computation of the negative curvature direction in large scale unconstrained problems. We describe a curvilinear method which uses a combination of a quasi-Newton direction and a negative curvature direction. We propose an algorithm for the computation of the search directions which uses information of two specific L-BFGS matrices in such a way that a...

Conjugate gradient methods are widely used for unconstrained optimization, especially large scale problems. Most of conjugate gradient methods don’t always generate a descent search direction, so the descent condition is usually assumed in the analyses and implementations. Dai and Yuan (1999) proposed the conjugate gradient method which generates a descent direction at every iteration. Yabe and...

In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve class of nonsmooth nonconvex composite optimization problems. We assume that the gradient smooth part objective function can only be approximated by oracles. The proposed combines general higher order steps derived from an underlying proximal type fixed-point equation with additional guarantee convergence. Ba...