A modified spectral PRP conjugate gradient method is presented for solving unconstrained optimization problems. The constructed search direction is proved to be a sufficiently descent direction of the objective function. With an Armijo-type line search to determinate the step length, a new spectral PRP conjugate algorithm is developed. Under some mild conditions, the theory of global convergenc...

In [Z.Wei, S. Yao, L. Liu, The convergence properties of some new conjugate gradient methods, Applied Mathematics and Computation 183 (2006) 1341–1350], Wei et al. proposed a new conjugate gradient method called WYL method which has good numerical experiments and some excellent properties such as b k P 0. In this paper, we prove that while tk 6 1 c 2L kgkk kdkk , the sufficient descent conditio...

Abstract: In this study, we study the application of a kind of nonmonotone line search in BFGS algorithm for solving unconstrained optimization problems. This nonmonotone line search is belongs to Armijo-type line searches and when the step size is being computed at each iteration, the initial test step size can be adjusted according to the characteristics of objective functions. The global con...

We propose a descent method via gap functions for solving nonsmooth variational inequalities with a locally Lipschitz operator. Assuming monotone operator (not necessarily strongly monotone) and bounded domain, we show that the method with an Armijo-type line search is globally convergent. Finally, we report some numerical experiments.

So this small package arrives at my office, addressed to “Anniken Goldstein.” Two Goldsteins work in my office, my Bride/Empress and myself, so she took the liberty of opening it up, and extracting a Darth Vader head coffee cup from a carefully bundled straw package. There was no accompanying note; the return address indicated that none was needed. Everyone from my receptionist to my office man...

In this paper a modified algorithm for solving the split feasibility problem (SFP) is presented. This algorithm uses the generalized Armijo line search in computing predictor step size and gives a correction step rule in the iterative process, which makes an accelerated convergence to the solution of SFP. Meanwhile, it needs not to compute the matrix inverses and the large eigenvalue of the mat...

Beam search (BS) is used as a heuristic to solve various combinatorial optimization problems, ranging from scheduling to assembly line balancing. In this paper, we develop a backtracking and an exchange-of-information (EOI) procedure to enhance the traditional beam search method. The backtracking enables us to return to previous solution states in the search process with the expectation of obta...

In this paper, by minimizing the distance between CG direction and of improved Perry conjugate gradient method [Yao et al., Numer. Algorithms 78 (2018) 1255–1269], we propose a descent modified HS method. A remarkable property is that it can produce sufficient property, which independent line search used. Under suitable conditions, prove with standard Armijo globally convergent for uniformly co...