The problem of solving a set of linear equations with a symmetric positive definite matrix is equivalent to the problem of minimizing a quadratic function. Consider the problem of finding x ∈ Rn satisfying
, where A ∈ Rn × n, b ∈ Rn and A is symmetric positive definite. The solution to this problem is also a solution of the optimization problem (P):
. Consider the point x̄ such that
. We can show that (1.2) are the necessary optimality conditions for problem (1.1).
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© 2009 Springer-Verlag Berlin Heidelberg
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(2009). Conjugate Direction Methods for Quadratic Problems. In: Conjugate Gradient Algorithms in Nonconvex Optimization. Nonconvex Optimization and Its Applications, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85634-4_1
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DOI: https://doi.org/10.1007/978-3-540-85634-4_1
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