A class of scaled gradient projection methods for optimization problems with simple constraints is considered. These iterative algorithms can be useful in variational approaches to image deblurring that lead to minimize convex nonlinear functions subject to nonnegativity constraints and, in some cases, to an additional flux conservation constraint. A special gradient projection method is introd...

W i tzgal l [ 7 L comment ing on the gradient project ion methods of R . Frlsch and J . B . Rosen , states: "More or less a l l algori thms for solving the l inear programming problem are known to be modificat ions of an algori thm for matrix inversion . Thus the simplex method corresponds to the Gauss-Jordan method . The methods of Frisch and Rosen are based on an interest ing method for inver...

The gradient projection algorithm for function minimization is often implemented using an approximate local minimization along the projected negative gradient. On the other hand, for some difficult combinational optimization problems, where a starting guess may be far from a solution, it may be advantageous to perform a nonlocal (exact) line search. In this paper we show how to evaluate the pie...

In this work, we propose a simple yet effective gradient projection algorithm for a class of stochastic optimal control problems. The basic iteration block is to compute gradient projection of the objective functional by solving the state and co-state equations via some Euler methods and by using the Monte Carlo simulations. Convergence properties are discussed and extensive numerical tests are...

Recently, adaptive beamforming has been widely used in wireless communications, microphone array speech processing and so on. One of the adaptive beamforming methods is directionally constrained minimization of power. However, this method is known to degrade if some of underlying assumptions on the environment, sources, or sensor array become violated [5]. To resolve this disadvantage, some met...

This paper considers some aspects of a gradient projection method proposed by Goldstein [l], Levitin and Polyak [3], and more recently, in a less general context, by McCormick [lo]. We propose and analyze some convergent step-size rules to be used in conjunction with the method. These rules are similar in spirit to the efficient Armijo rule for the method of steepest descent and under mild assu...

We study an equivalent optimization problem with an inequality constraint and boundary conditions, whose necessary condition for the optimality is the variational inequality presentation of American options. To solve the problem, we use the gradient projection method, with discretizations both in time and space. We tested the algorithm and compared with the projective successive over-relaxation...

We consider an optimal control problem for systems governed by a highly nonlinear second order elliptic partial differential equation, with control and state constraints. The problem is formulated in the classical and in the relaxed form, and various necessary conditions for optimality are given. For the numerical solution of these problems, we propose a penalized gradient projection method gen...

The aim of this paper is to study the convergence properties of the gradient projection method and to apply these results to algorithms for linearly constrained problems. The main convergence result is obtained by defining a projected gradient, and proving that the gradient projection method forces the sequence of projected gradients to zero. A consequence of this result is that if the gradient...