en عمومى General پژوهشي Research paper <div dir="ltr">In this paper, we present a nonmonotone trust-region algorithm for&nbsp;unconstrained optimization. We first introduce a variant of the&nbsp;nonmonotone strategy proposed by Ahookhosh and Amini cite{AhA&nbsp;01} and incorporate it into the trust-region framework to&nbsp;construct a more efficient approach. Our new nonmonotone strategy&nbsp;combines the current function value with the maximum function&nbsp;values in some prior successful iterates. For iterates far away<br> from the optimizer, we give a very strong nonmonotone strategy. In&nbsp;the vicinity of the optimizer, we have a weaker nonmonotone&nbsp;strategy. It leads to a medium nonmonotone strategy when iterates&nbsp;are not far away from or close to the optimizer. Theoretical&nbsp;analysis indicates that the new approach converges globally to a&nbsp;first-order critical point under classical assumptions. In&nbsp;addition, the local convergence is also studied. Extensive&nbsp;numerical experiments for unconstrained optimization problems are&nbsp;reported.</div> Unconstrained optimization, Trust-region framework, Nonmonotone technique, Theoretical convergence 15 33 http://ijmsi.ir/browse.php?a_code=A-10-3031-1&slc_lang=en&sid=1 M. kimiaei kimiaeim83@univie.ac.at 10031947532846008764 10031947532846008764 Yes Vienna University H. esmaeili esmaeili47@yahoo.com 10031947532846008765 10031947532846008765 No Bu Ali University F. rahpeymaii rahpeyma_83@yahoo.com 10031947532846008766 10031947532846008766 No Payame Noor