In this dissertation an approach to multistep algorithms on constrained optimisation problems is discussed. Constraints will be given by algebraic manifolds, therefore the manifold will be also be an affine variety. Algorithms for moving along geodesics, parallel transport of previous search and descend directions and the logarithmic problems are developed. Then those are tested together with the steepest descent method, a conjugate gradient method and BFGS algorithm on test functions from the CUTEr/st problem set.
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