We consider the Spectral Projected Gradient method for solving constrained optimization porblems with the objective function in the form of mathematical expectation. It is assumed that the feasible set is convex, closed and easy to project on. The objective function is approximated by a sequence of Sample Average Approximation functions with different sample sizes. The sample size update is bas...

The poor practical behavior of (1)-(2) has been known for many years. If the level sets of f resemble long valleys, the sequence {xk} displays a typical zig-zagging trajectory and the speed of convergence is very slow. In the simplest case, in which f is a strictly convex quadratic, the method converges to the solution with a Q-linear rate of convergence whose factor tends to 1 when the conditi...

A study of the convergence properties of spectral projected subgradient method is presented and the convergence is shown. The convergence is based on spectral projected gradient approach. Some updates of the spectral projected subgradient are described.

The spectral gradient method has proved to be effective for solving large-scale unconstrained optimization problems. It has been recently extended and combined with the projected gradient method for solving optimization problems on convex sets. This combination includes the use of nonmonotone line search techniques to preserve the fast local convergence. In this work we further extend the spect...

We study and analyze a nonmonotone globally convergent method for minimization on closed sets. This method is based on the ideas from trust-region and Levenberg-Marquardt methods. Thus, the subproblems consists in minimizing a quadratic model of the objective function subject to a given constraint set. We incorporate concepts of bidiagonalization and calculation of the SVD “with inaccuracy” to ...

A spectral-projected gradient method and an extension of the Kubelka-Munk theory are applied to obtain the relevant parameters of the theory from measured diffuse reflectance spectra of pigmented samples illuminated with visible diffuse radiation. The initial estimate of the spectral dependence of the parameters, required by a recursive spectral-projected gradient method, was obtained by use of...