Global convergence analysis of a modified conjugate gradient method for unconstrained optimization problems

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  • What: And the authors provide numerical experiments to illustrate its effectiveness and efficiency in solving unconstrained optimization problems. The authors propose a new π›½π‘˜ defined by: π›½π‘˜πΈπ΄= FJS Next, the authors show that it holds true for π‘˜ β‰₯ 1 Multiply by π‘”π‘˜+1 to get 𝑇 π‘‘π‘˜+1 π‘”π‘˜+1=π‘”π‘˜+1 (-π‘”π‘˜+1 + π›½π‘˜πΈπ΄ π‘‘π‘˜π‘‡ )=-β€–π‘”π‘˜+1 β€–2 + π›½π‘˜πΈπ΄ π‘‘π‘˜π‘‡ π‘”π‘˜+1 ‖𝑔 β€– π‘˜ 𝑇 β€–π‘”π‘˜ β€–2 - β€–π‘”π‘˜-1 β€– π‘”π‘˜ π‘”π‘˜-1 𝑇=-β€–π‘”π‘˜+1 β€–2 + π‘”π‘˜+1 π‘‘π‘˜ β€–π‘‘π‘˜-1 β€–2 - π‘”π‘˜π‘‡ π‘‘π‘˜-1 Assumption A (𝔦) Proof; the authors show that π›½π‘˜πΈπ΄ is always not negative.
  • Who: F.O. from the Nigeria Department of Mathematics, Federal University Dutse (FUD), PM.B. , Dutse, Jigawa State, Nigeria. have published the Article: online: GLOBAL CONVERGENCE ANALYSIS . . .

     

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