Geodesic
A Discrete Projection Quasi Newton Method for Linearly Constrained Problems
Yugoslav journal of operations research, Tome 5 (1995) no. 2, p. 221 .

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In this paper we define a discrete quasi -Newton algorithm which uses only function values for finding an optimal solution to the problem $min \{ \phi(x) \| x \in X \}$, where X is a convex polytope. It is shown that using this algorithm one can reduce the initial problem to a finite number of subproblems of the type $min \{ \phi(x) \| x \in C \}$, where C is a linear manifold . It is also shown that each cluster point of the sequence gene rated by the algorithm is an optimal point of the considered optimization problem.
Keywords: Linear inequality-constrained minimization, Discrete quasi-Newton method, Projected gradient, Cholesky factortzation 
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     author = {Nada I. {\DJ}uranovi\'c - Mili\v{c}i\'c},
     title = {A {Discrete} {Projection} {Quasi} {Newton} {Method} for {Linearly} {Constrained} {Problems}},
     journal = {Yugoslav journal of operations research},
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     year = {1995},
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Nada I. Đuranović - Miličić. A Discrete Projection Quasi Newton Method for Linearly Constrained Problems. Yugoslav journal of operations research, Tome 5 (1995) no. 2, p. 221 . http://geodesic.mathdoc.fr/item/YJOR_1995_5_2_a4/