Titlebook: Conjugate Gradient Algorithms in Nonconvex Optimization; Rados?aw Pytlak Book 2009 Springer-Verlag Berlin Heidelberg 2009 Algebra.Bound Co

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978-3-642-09925-0Springer-Verlag Berlin Heidelberg 2009

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Conjugate Direction Methods for Quadratic Problems,tion. Consider the problem of finding . ∈ . satisfying ., where . ∈ ., . ∈ . and . is symmetric positive definite. The solution to this problem is also a solution of the optimization problem (.): .. Consider the point x? such that .. We can show that (1.2) are the necessary optimality conditions for problem (1.1).

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Conjugate Gradient Methods for Nonconvex Problems,us chapter a conjugate gradient algorithm is an iterative process which requires at each iteration the current gradient and the previous direction. The simple scheme for calculating the current direction was easy to extend to a nonquadratic problem ..

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https://doi.org/10.1007/3-540-36416-1inear Hestenes-Stiefel algorithm provided that the directional minimization is exact. Having that in mind and the fact that Hager and Zhang do not stipulate condition (2.68) in Theorem 2.14 their main convergence result is remarkable.