A Regularized Gradient Projection Method for the Minimization Problem

A Regularized Gradient Projection Method for the Minimization Problem

Regularized gradient-projection methods for finding the minimum-norm solution of the constrained convex minimization problem

Let H be a real Hilbert space and C be a nonempty closed convex subset of H. Assume that g is a real-valued convex function and the gradient ∇g is [Formula: see text]-ism with [Formula: see text]. Let [Formula: see text], [Formula: see text]. We prove that the sequence [Formula: see text] generated by the iterative algorithm [Formula: see text], [Formula: see text] converges strongly to [Formul...

A coordinate gradient descent method for ℓ1-regularized convex minimization

In applications such as signal processing and statistics, many problems involve finding sparse solutions to under-determined linear systems of equations. These problems can be formulated as a structured nonsmooth optimization problems, i.e., the problem of minimizing `1-regularized linear least squares problems. In this paper, we propose a block coordinate gradient descent method (abbreviated a...

The Gradient Projection Method for Solving an Optimal Control Problem

A gradient method for solving an optimal control problem described by a parabolic equation is considered. The gradient projection method is applied to solve the problem. The convergence of the projection algorithm is investigated.

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.