Solving unconstrained optimization problems via hybrid CD-DY conjugate gradient methods with applications

In this work, a new hybrid conjugate gradient (CG) algorithm is developed for finding solutions to unconstrained optimization problems. The search direction of the algorithm consists of a combination of conjugate descent (CD) and Dai–Yuan (DY) CG parameters. The search direction is also close to the direction of the memoryless Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton algorithm. Moreover, the search direction is bounded and satisfies the descent condition independent of the line search. The global convergence of the algorithm under the Wolfe-type is proved with the help of some proper assumptions. Numerical experiments on some benchmark test problems are reported to show the efficiency of the new algorithm compared with other existing schemes. Finally, application of the algorithm in risk optimization completes the work.