Search

In this paper, we present a trust region algorithm with memory for equality constrained optimization problems. Different from the traditional trust region algorithms, our trust region model includes memory of the past iterations, which makes the algorithm more farsighted in the sense that its behavior is not completely dominated by the local nature of the objective function, but rather by a more global view. The global convergence is established by using a nonmonotone technique. We report numerical tests to examine the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this article, unconstrained minimax problems are discussed, and a sequential quadratic programming (SQP) algorithm with a new nonmonotone linesearch is presented. At each iteration, a search direction of descent is obtained by solving a quadratic programming (QP). To circumvent the Maratos effect, a high-order correction direction is achieved by solving another QP and a new nonmonotone linesearch is performed. Under reasonable conditions, the global convergence and the rate of superlinear convergence are established. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

SupposeEis a uniformly smooth real Banach space andF,K:E → Eare bounded accretive maps withD(K) = F(E) = E. Assume that the Hammerstein equationu + KFu = 0 has a solutionu*. Anexplicit simple iteration processis shown to converge strongly tou*. No invertibility or continuity assumption is imposed onK. Our theorems are significant improvements on important recent results (e.g. [11]). [ABSTRACT FROM PUBLISHER]

By means of a conjugate gradient strategy, we propose a trust region method for unconstrained optimization problems. The search direction is an adequate combination of the conjugate gradient direction and the trust-region direction. The global convergence and the quadratic convergence of this method are established under suitable conditions. Numerical results show that the presented method is competitive to the trust region method and the conjugate gradient method. [ABSTRACT FROM AUTHOR]

We derive strongly convergent algorithms to solve inverse problems involving elastic-net regularization. Moreover, using functional analysis techniques, we provide a rigorous study of the asymptotic properties of the regularized solutions that allows to cast in a unified framework ℓ1, elastic-net and classical Tikhonov regularization. [ABSTRACT FROM AUTHOR]