An iterative algorithm is proposed for minimizing a convex function on a set defined as the set-theoretic difference between a convex set and the union of several convex sets. The convergence of the algorithm is prove...
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An iterative algorithm is proposed for minimizing a convex function on a set defined as the set-theoretic difference between a convex set and the union of several convex sets. The convergence of the algorithm is proved in terms of necessary conditions for a local minimum.
We consider an algorithm with space dilation. For a certain choice of the dilation coefficient, this is a method of outer approximation of semi-ellipsoids by ellipsoids with monotonous decrease in their volume. It is ...
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ISBN:
(纸本)9783030386030;9783030386023
We consider an algorithm with space dilation. For a certain choice of the dilation coefficient, this is a method of outer approximation of semi-ellipsoids by ellipsoids with monotonous decrease in their volume. It is shown that the Yudin-Nemirovski-Shor ellipsoid method is a specific case. Two forms of the algorithm are dealt with: the B-form, where the inverse space transformation matrix B is updated, and the H-form, where the symmetric matrix H = BB inverted perpendicular is updated. Our test results show that the B-form of the algorithm is computationally more robust to error accumulation than the H-form. The application of the algorithm for finding a minimizer of a convex function, for solving convex programming problems, and for determining a saddle point of a convex-concave function is described. Possible ways of accelerating the algorithm by deeper ellipsoid approximations are discussed as well.
In this paper, a joint transmitter and receiver beamformers design algorithm for downlink multiple input multiple output multicarrier code-division multiple access (MIMO MC-CDMA) system is proposed. The algorithm is i...
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ISBN:
(纸本)9780780393899
In this paper, a joint transmitter and receiver beamformers design algorithm for downlink multiple input multiple output multicarrier code-division multiple access (MIMO MC-CDMA) system is proposed. The algorithm is iterative in nature where the transmitter beamformers and the receiver beamformers are determined alternately. The transmitter beamforming problem with a given receiver beamformer is formulated as a convex programming problem, which can be solved optimally using second order cone programming (SOCP), while the receiver beamforming problem is formulated as a constrained optimization problem with an analytical solution. The convergence of the algorithm is analyzed and the performance of the proposed algorithm is evaluated by computing simulation.
A problem of plane elastic-plastic stress is connected with a varitional problem in an appropriate Hilbert space. Next, the numerical solution of the latter is considered. Finally, the exact and the approximate soluti...
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We study an infinite dimensional mathematical programmingproblem, which arises naturally in solid mechanics. It concerns the moment of collapse, and the collapse state itself, of a plastic structure subjected to incr...
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The penalty methods constitute a family of particularly interesting algorithms of the two points of view: the simpleness of principle and the practical efficiency. They are considered as ill-conditioned because the pe...
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The penalty methods constitute a family of particularly interesting algorithms of the two points of view: the simpleness of principle and the practical efficiency. They are considered as ill-conditioned because the penalty parameter r(k) tends to infinity, as k tends infinity. It is what led to us to introduce what we call augmented Lagrangian to regularize the solutions. Namely, to avoid the numerical instability of the classical penalty method. Another favors of the augmented Lagrangian is that by presence of the term lambda(i) g(i), the exact solution of the problem can be determined without making aim rk towards the infinity, contrary to the penalty method, where it has the effect of diverting the packaging of the problem to be resolved. The using of augmented Lagrangian is considered as an improvement of the penalty methods. It avoids having to use too big parameters of penalties. Besides, the fact of adding the quadratic term r(k)(g(+))(2) k in the Lagrangian will improve the properties of convergence of the algorithms of duality in this paper. In this paper, we study some augmented Lagrangian algorithms applied to convex nondiff erentiable optimization problems and prove their convergence.
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