An $$O(\sqrt n L)$$ iteration bound primal-dual cone affine scaling algorithm for linear programmingiteration bound primal-dual cone affine scaling algorithm for linear programming
نویسندگان
چکیده
منابع مشابه
An O(root(n)L) iteration bound primal-dual cone affine scaling algorithm for linear programming
In this paper we introduce a primal-dual affine scaling method. The method uses a search-direction obtained by minimizing the duality gap over a linearly transformed conic section. This direction neither coincides with known primal-dual affine scaling directions (Jansen et al., 1993; Monteiro et al., 1990), nor does it fit in the generic primal-dual method (Kojima et al., 1989). The new method ...
متن کاملAn O(√nL) Iteration Bound Primal-Dual Cone Affine Scaling Algorithm for Linear Programming
In this paper we introduce a primal-dual affine scaling method. The method uses a searchdirection obtained by minimizing the duality gap over a linearly transformed conic section. This direction neither coincides with known primal-dual affine scaling directions [12, 21], nor does it fit in the generic primal-dual method [15]. The new method requires O(√nL) main iterations. It is shown that the ...
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Semide nite programming concerns the problem of optimizing a linear function over a section of the cone of semide nite matrices In the cone a ne scaling approach we replace the cone of semide nite matrices by a certain inscribed cone in such a way that the resulting optimization problem is analytically solvable The now easily obtained solution to this modi ed problem serves as an approximate so...
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In this paper, we give an example of a semidefinite programming problem in which primal-dual affine-scaling algorithms using the HRVW/KSH/M, MT, and AHO directions fail. We prove that each of these algorithm can generate a sequence converging to a non-optimal solution, and that, for the AHO direction, even its associated continuous trajectory can converge to a non-optimal point. In contrast wit...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 1996
ISSN: 0025-5610,1436-4646
DOI: 10.1007/bf02592088