continuous algorithms are proposed and studied for solution of convex programming problems and for finding the saddle points of convex-concave functions by the use of projection. The theory of monotone operators, conv...
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This paper provides a brief description on how continuous algorithms can be applied to binary problems. Differential Evolution is the continuous algorithm studied and two versions of this algorithm are presented: the ...
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ISBN:
(纸本)9781479931941
This paper provides a brief description on how continuous algorithms can be applied to binary problems. Differential Evolution is the continuous algorithm studied and two versions of this algorithm are presented: the Binary Differential Evolution with a binary encoding and the Discretized Differential Evolution with a continuous encoding. Several discretization methods are presented and the most used method in literature is implemented for the solution discretization. Benchmarks with different complexity and search space sizes of the Multiple Knapsack Problem are used to compare the performance of each Differential Evolution algorithm presented and the Genetic Algorithm with binary encoding. Results suggest that continuous methods can be very efficient when discretized for binary spaces.
Sliding modes are used to analyze a class of dynamical systems that solve convex programming problems. The analysis is carried out using concepts from the theory of differential equations with discontinuous right-hand...
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Sliding modes are used to analyze a class of dynamical systems that solve convex programming problems. The analysis is carried out using concepts from the theory of differential equations with discontinuous right-hand sides and Lyapunov stability theory. It is shown that the equilibrium points of the system coincide with the minimizers of the convex programming problem, and that irrespective of the initial state of the system the state trajectory converges to the solution set of the problem. The dynamic behavior of the systems is illustrated by two numerical examples.
Within a Hilbert space we consider nonsmooth convex programs with sharp constraints. Examples include all problem instances that are bounded and strictly feasible. To solve such programs we pursue an absolutely contin...
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Within a Hilbert space we consider nonsmooth convex programs with sharp constraints. Examples include all problem instances that are bounded and strictly feasible. To solve such programs we pursue an absolutely continuous trajectory generated by a differential inclusion of subgradient type. Whenever this inclusion offers some freedom of choice, we select a steepest descent direction. It is shown that the proposed algorithm converges to an optimal solution in finite time.
Numerical mathematics is viewed as the analysis of continuous algorithms. Four of the components of numerical mathematics are discussed. These are: foundations (finite precision number systems, computational complexit...
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Numerical mathematics is viewed as the analysis of continuous algorithms. Four of the components of numerical mathematics are discussed. These are: foundations (finite precision number systems, computational complexity), synthesis and analysis of algorithms, analysis of error, programs and program libraries. [ABSTRACT FROM AUTHOR]
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