Mathematically testing the validity of a theoretical model with an observed physical system is an important step in understanding and utilizing such a system. Perhaps even more useful is the generation of computationa...
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Mathematically testing the validity of a theoretical model with an observed physical system is an important step in understanding and utilizing such a system. Perhaps even more useful is the generation of computational techniques which use input-output data from physical systems to automatically construct mathematical models which, in some sense, provide the ''best'' descriptions of the real systems. This paper briefly discusses a few of the more recent mathematical techniques available for model generation and testing. A new identification method based upon convex and linear programming is discussed in detail and a number of examples indicating its applicability are given. The linear programming method is basically an approximation to a convex programming problem, the solution of which determines the coefficients of the differential equation describing the observed system data. A number of extensions of the identification method indicate some of its most useful properties. The order of the assumed model differential equation can be larger than that of the unknown system and the identification process will either assign zero values to the superfluous coefficients of the model or pole-zero cancellations will occur in the factored form of the Laplace transform of the model transfer function. ''Best'' lowest order models may be selected automatically. Linear constraints among the coefficients of the model differential equation may be used to restrict the allowable ranges of the coefficients. Multiple sets of data for a single system may be used simultaneously in the indentification process. Multiple input-output systems or systems described by difference equations or with transportation lag can also be identified. Coefficients of time varying and/or nonlinear models may be determined. Review on some recent identification methods and a new convex and linear programming method is presented which is particularly applicable to biological and medical experimentation.
A numerical algorithm for minimizing a convex function on the set-theoretic intersection of a spherical surface and a convex compact set is proposed. The idea behind the algorithm is to reduce the original minimizatio...
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A numerical algorithm for minimizing a convex function on the set-theoretic intersection of a spherical surface and a convex compact set is proposed. The idea behind the algorithm is to reduce the original minimization problem to a sequence of convex programming problems. Necessary extremum conditions are examined, and the convergence of the algorithm is analyzed.
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.
An algorithm with space dilation is presented, which is the circumscribed ellipsoid method under a certain choice of dilation coefficient. It is shown that its special case is the Yudin-Nemirovsky-Shor ellipsoid metho...
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An algorithm with space dilation is presented, which is the circumscribed ellipsoid method under a certain choice of dilation coefficient. It is shown that its special case is the Yudin-Nemirovsky-Shor ellipsoid method. The application of the algorithm to solving a convex programming problem and the problem of finding a saddle point of a convex-concave function are described.
Numerical methods for solving a convex programming problem are considered whose guaranteed convergence rate depends only on the space dimension. On average, the ratio of the corresponding geometric progression is bett...
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Numerical methods for solving a convex programming problem are considered whose guaranteed convergence rate depends only on the space dimension. On average, the ratio of the corresponding geometric progression is better than that in the basis model of ellipsoids or simplexes. Results of numerical experiments are presented.
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.
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.
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.
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