Characterizations of optimal linear supports and approximates in realn-dimensional space are derived. We first characterize anL 1-support; that is, a support hyperplane for a continuous function, over a solid, compact...
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Characterizations of optimal linear supports and approximates in realn-dimensional space are derived. We first characterize anL 1-support; that is, a support hyperplane for a continuous function, over a solid, compact set, which is optimal in theL 1-sense. We then characterize best approximates; that is, affinely linear functions which are the best approximates to a continuous function on a compact set by some optimality criterion. The characterization is first derived under the Natural criterion and then expanded to the Chebyshev criterion, utilizing Geoffrion's Criterion Equivalence.
A numerical algorithm for minimizing a convex function on a smooth surface is proposed. The algorithm is based on reducing the original problem to a sequence of convex programming problems. Necessary extremum conditio...
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A numerical algorithm for minimizing a convex function on a smooth surface is proposed. The algorithm is based on reducing the original problem to a sequence of convex programming problems. Necessary extremum conditions are examined, and the convergence of the algorithm is analyzed.
A numerical algorithm is proposed for minimizing a convex function on the set-theoretic difference between a set of points of a smooth surface and the union of finitely many convex open sets in n-dimensional Euclidean...
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A numerical algorithm is proposed for minimizing a convex function on the set-theoretic difference between a set of points of a smooth surface and the union of finitely many convex open sets in n-dimensional Euclidean space. The idea behind the algorithm is to reduce the original problem to a sequence of convex programming problems. Necessary extremum conditions are examined, and the convergence of the algorithm is analyzed.
An inscribed ellipsoid method is considered for solving a convex programming problem with linear constraints. A new approximate solution is obtained by using the minimizer of the objective function on the current elli...
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An inscribed ellipsoid method is considered for solving a convex programming problem with linear constraints. A new approximate solution is obtained by using the minimizer of the objective function on the current ellipsoid of the maximum volume. It is shown that the number N(epsilon) of iterations needed to achieve an accuracy epsilon in the n-dimensional space of feasible solutions is determined by an inequality N(epsilon) less than or equal to n . log(2)(1/epsilon). One can consider the proposed algorithm as a proof of the existence of a method which has the same estimation of complexity as a dichotomy, and therefore, is theoretically not improvable.
Chebyshev points of bounded convex sets, search algorithms for them, and various applications to convexprogramming are considered for simple approximations of reachable sets, optimal control, global optimization of a...
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Chebyshev points of bounded convex sets, search algorithms for them, and various applications to convexprogramming are considered for simple approximations of reachable sets, optimal control, global optimization of additive functions on convex polyhedra, and integer programming. The problem of searching for Chebyshev points in multicriteria models of development and operation of electric power systems is considered.
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.
The thought to put forward a queuing model proposed in this work was its pertinence in everyday life wherever we can see the uses of computing and networking systems. Industrial software developers and system managers...
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The thought to put forward a queuing model proposed in this work was its pertinence in everyday life wherever we can see the uses of computing and networking systems. Industrial software developers and system managers can consider the results of the model to evolve their system for better results. Here we present a novel queueing model having erratic server with delayed repair and balking. Two distinct breakdowns i.e. active and passive breakdown for the system are also considered with their respective amendments. This model is closely related with the smooth functioning of the system during some internal faults (virus attack, electricity failures etc.). The performance indicators which are utilized in enhancing the service standards are obtained using supplementary variable technique. Using ANFIS soft computing technique we have compared the analytical results with those of neuro fuzzy results. Furthermore single and bi-objective minimization problems are considered and minima is obtained using particle swarm optimization and multi objective genetic algorithm respectively. Also, the minimization problems are shown as a convex programming problem to ensure the global optimality of the result. The proposed approach makes it conceivable to accomplish a relevant harmony between operational expenses and administration quality.
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.
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.
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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