A hybrid of adjustable trust-region and nonmonotone algorithms for unconstrained optimization

作者：Amini Keyvan^*; Ahookhosh Masoud

来源：Applied Mathematical Modelling, 2014, 38(9-10): 2601-2612.

DOI：10.1016/j.apm.2013.10.062

• Unconstrained optimization
• Trust-region framework
• Nonmonotone strategy
• Adjustable radius
• Global convergence

This study devotes to incorporating a nonmonotone strategy with an automatically adjusted trust-region radius to propose a more efficient hybrid of trust-region approaches for unconstrained optimization. The primary objective of the paper is to introduce a more relaxed trust-region approach based on a novel extension in trust-region ratio and radius. The next aim is to employ stronger nonmonotone strategies, i.e. bigger trust-region ratios, far from the optimizer and weaker nonmonotone strategies, i.e. smaller trust-region ratios, close to the optimizer. The global convergence to first-order stationary points as well as the local superlinear and quadratic convergence rates are also proved under some reasonable conditions. Some preliminary numerical results and comparisons are also reported.

• 出版日期2014-5-1