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Metody vnitřních bodů pro zobecněnou minimaxovou optimalizaci
Lukšan, Ladislav ; Matonoha, Ctirad ; Vlček, Jan
A new class of primal interior point methods for generalized minimax optimization is described. These methods use besides a standard logarithmic barrier function also barrier functions bounded from below which have more favourable properties for investigation of global convergence. It deals with descent direction methods, where an approxmation of the Hessian matrix is computed by gradient differences or quasi-Newton updates. Two-level optimization is used. A direction vector is computed by a Choleski decompostition of a sparse matrix. Numerical experiments concerning two basic applications, minimization of a point maximum and a sum of absolute values of smooth functions, are presented.
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Metoda vnitřních bodů pro velkou řídkou l1 optimalizaci
Lukšan, Ladislav ; Matonoha, Ctirad ; Vlček, Jan
In this paper, we propose an interior-point method for large sparse l1 optimization. After a short introduction, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Thus relatively difficult l1 optimization problems can be solved successfully. The results of computational experiments given in this paper confirm efficiency and robustness of the proposed method
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