In most crop breeding programs, the rate of yield increment is insufficient to cope with the increased food demand caused by a rapidly expanding global population. In plant breeding, the development of improved crop varieties is limited by the very long crop duration. Given the many phases of crossing, selection, and testing involved in the production of new plant varieties, it can take one or two decades to create a new cultivar. One possible way of alleviating food scarcity problems and increasing food security is to develop improved plant varieties rapidly. Traditional farming methods practiced since quite some time have decreased the genetic variability of crops. To improve agronomic traits associated with yield, quality, and resistance to biotic and abiotic stresses in crop plants, several conventional and molecular approaches have been used, including genetic selection, mutagenic breeding, somaclonal variations, whole-genome sequence-based approaches, physical maps, and functional genomic tools. However, recent advances in genome editing technology using programmable nucleases, clustered regularly interspaced short palindromic repeats (CRISPR), and CRISPR-associated (Cas) proteins have opened the door to a new plant breeding era. Therefore, to increase the efficiency of crop breeding, plant breeders and researchers around the world are using novel strategies such as speed breeding, genome editing tools, and high-throughput phenotyping. In this review, we summarize recent findings on several aspects of crop breeding to describe the evolution of plant breeding practices, from traditional to modern speed breeding combined with genome editing tools, which aim to produce crop generations with desired traits annually.
In this paper, we are concerned with the conjugate gradient methods for solving unconstrained optimization problems. It is well-known that the direction generated by a conjugate gradient method may not be a descent direction of the objective function. In this paper, we take a little modification to the Fletcher-Reeves (FR) method such that the direction generated by the modified method provides a descent direction for the objective function. This property depends neither on the line search used, nor on the convexity of the objective function. Moreover, the modified method reduces to the standard FR method if line search is exact. Under mild conditions, we prove that the modified method with Armijo-type line search is globally convergent even if the objective function is nonconvex. We also present some numerical results to show the efficiency of the proposed method.
Mathematics Subject Classification (2000) 90C30 · 65K05Supported by the 973 project (2004CB719402) and the NSF foundation (10471036) of China.
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