This paper addresses the multi-objective strongly convex optimization problem by designing a fixed-time optimization based on second-order integral multi-agent systems. The proposed algorithm includes a two-stage opti...
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ISBN:
(数字)9789887581581
ISBN:
(纸本)9798350366907
This paper addresses the multi-objective strongly convex optimization problem by designing a fixed-time optimization based on second-order integral multi-agent systems. The proposed algorithm includes a two-stage optimization *** the first stage, each agent has a local objective controller that is designed to make each agent converge to the optimal state that minimizes respective local costfunctions in a fixed ***, the local optimal state obtained in the first stage is used as the initial state of the global objective controller, which allows to construct the global objective controller that makes the multiple agents' states reach consensus in terms of the information interaction between neighboring agents and the Hessian matrix of the local cost function, where the consistency state is the global optimal state. In addition, the above optimization process is proved by the Lyapunov theory. Note that the designed controllers are not dependent on the initial state of the agents so that various tasks can be adapted. Finally, numerical simulation results are given to demonstrate the effectiveness of the proposed algorithm.
We propose a new family of vector similarity measures. Each measure is associated with a convexcost function. Given two vectors, we determine the surface normals of the convex function at the vectors. The angle betwe...
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We propose a new family of vector similarity measures. Each measure is associated with a convexcost function. Given two vectors, we determine the surface normals of the convex function at the vectors. The angle between the two surface normals is the similarity measure. convexcost function can be the negative entropy function, total variation (TV) function and filtered variation function constructed from wavelets. The convex cost functions need not to be differentiable everywhere. In general, we need to compute the gradient of the cost function to compute the surface normals. If the gradient does not exist at a given vector, it is possible to use the sub-gradients and the normal producing the smallest angle between the two vectors is used to compute the similarity measure. The proposed measures are compared experimentally to other nonlinear similarity measures and the ordinary cosine similarity measure. The TV-based vector product is more energy efficient than the ordinary inner product because it does not require any multiplications.
Economic dispatch aims to make the minimal operating cost of power plant by determining the optimal power produced by each generating unit under constrained circumstances. At the present time, power utilities have stu...
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Economic dispatch aims to make the minimal operating cost of power plant by determining the optimal power produced by each generating unit under constrained circumstances. At the present time, power utilities have stumble upon a fresh dispatch problem, because of crucial concern over fuel shortages. Fuel suppliers increase constraints in their fuel supply contracts that force the utilities to schedule the generation on the basis of fuel availability. With the ever increasing proportion of the fuel budget in the total operating costs, the fuel restricted economic dispatch problem has popped up. A new methodology based on a teaching learning-based optimization algorithm is proposed for solving fuel restricted economic dispatch problems. The potential of the proposed method is tested with standard test systems which include different cost characteristics. The obtained results are compared to other algorithms surfaced in the recent state-of-the-art literature, confirming the effectiveness of the developed methodology.
This paper deals with the problem of finding a minimum cost schedule for a set of dependent activities when a convexcost function is attached to the starting time of each activity. A first optimality necessary and su...
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This paper deals with the problem of finding a minimum cost schedule for a set of dependent activities when a convexcost function is attached to the starting time of each activity. A first optimality necessary and sufficient condition bearing on the head and tail blocks of a schedule is first established. A second such condition that uses the spanning active equality trees of a schedule leads to design a generic algorithm for the general case. When the cost function is the usual earliness-tardiness linear function with assymetric and independent penalty coefficients, the problem is shown to be solved in O(nmax{n,m}). Finally, the special cases when the precedence graph is an intree or a family of chains are then also shown to be solved by efficient polynomial algorithms. (C) 2002 Elsevier Science B.V. All rights reserved.
The probability of error of classification methods based on convex combinations of simple base classifiers by "boosting" algorithms is investigated. The main result of the paper is that certain regularized b...
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The probability of error of classification methods based on convex combinations of simple base classifiers by "boosting" algorithms is investigated. The main result of the paper is that certain regularized boosting algorithms provide Bayes-risk consistent classifiers under the sole assumption that the Bayes classifier may be approximated by a convex combination of the base classifiers. Nonasymptotic distribution-free bounds are also developed which offer interesting new insight into how boosting works and help explain its success in practical classification problems.
Existing blind adaptive equalizers that use nonconvex cost functions and stochastic gradient descent suffer from lack of global convergence to an equalizer setup that removes sufficient ISI when an FIR equalizer is us...
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Existing blind adaptive equalizers that use nonconvex cost functions and stochastic gradient descent suffer from lack of global convergence to an equalizer setup that removes sufficient ISI when an FIR equalizer is used. In this paper, we impose convexity on the cost function and anchoring of the equalizer away from the all-zero setup. We establish that there exists a globally convergent blind equalization strategy for 1-D pulse amplitude modulation (PAM) systems with bounded input data (discrete or continuous) even when the equalizer is truncated. The resulting cost function is a constrained l1 norm of the joint impulse response of the channel and the equalizer. Our results apply to arbitrary linear channels (provided there are no unit circle zeros) and apply regardless of the initial ISI (that is whether the eye is initially open or closed). We also show a globally convergent stochastic gradient scheme based on an implementable approximation of the l1 cost function.
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