In this paper, we present a new approach for solving absolute value equation (AVE) whichuse Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradientmethods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descentdir...

let $x$ be a reflexive banach space, $t:xto x$ be a nonexpansive mapping with $c=fix(t)neqemptyset$ and $f:xto x$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. in this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences t...

The exact steepest descent method was born in [AKT4] by combining the ordinary steepest descent method with the exact WKB analysis. (See, e.g., [AKT2] for the notion and notations of the exact WKB analysis used in this report.) It is a straightforward generalization of the ordinary steepest descent method and provides us with a new powerful tool for the description of Stokes curves as well as f...

Much recent attention has been devoted to gradient descent algorithms where the steepest descent step size is replaced by a similar one from a previous iteration or gets updated only once every second step, thus forming a faster gradient descent method. For unconstrained convex quadratic optimization these methods can converge much faster than steepest descent. But the context of interest here ...

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...

In this paper , we first extend and analyze the steepest descent method for solving optimal control problem for systems governed by Volterra integral equations . Then, we present some hybrid methods based on the extended steepest descent and two-step Newton methods, to solve the problem. The global convergence results are also established using some mild assumptions and conditions. Numerical re...