M.N. Vrahatis, G.S. Androulakis, J.N. Lambrinos and G.D. Magoulas, A class of gradient unconstrained minimization algorithms with adaptive stepsize, J. Comput. Appl. Math. 114 (2), 367--386, (2000). Home/Search Document Details and Download
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M.N. Vrahatis, G.S. Androulakis, J.N. Lambrinos and G.D. Magoulas, A class of gradient unconstrained minimization algorithms with adaptive stepsize, J. Comput. Appl. Math. 114 (2), 367--386, (2000).
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Vrahatis M.N., Androulakis G.S., Lambrinos J.N. and Magoulas G.D., A class of gradient unconstrained minimization algorithms with adaptive stepsize, J. Comput. Appl. Math., 114, No. 2, 367--386, (2000).
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M.N. Vrahatis, G.S. Androulakis, J.N. Lambrinos and G.D. Magoulas, A Class of Gradient Unconstrained Minimization Algorithms with Adaptive Stepsize, J. Comput. Appl. Math., 114(2), 2000, 367--386.
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M.N. Vrahatis, G.S. Androulakis, J.N. Lambrinos and G.D. Magoulas, "A Class of Gradient Unconstrained Minimization Algorithms with Adaptive Step Size", J. Comp. Appl. Math.,Vol. 114, 367--386, 2000.
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....convergence properties of all the above methods are well studied and analyzed (see, for example, 12] and to this end there are many theorems available in the literature. Furthermore, the above iterative linear schemes can be also extended to unconstrained optimization of a nonlinear function [27,28]. Although the nonlinear iterative rootfinding methods have been extensively studied, the unconstrained optimization case has not been thoroughly studied and analyzed. In this paper, we give some recent convergence and experimental results of ours related to the generalization of the iterative ....
M.N. Vrahatis, G.S. Androulakis, J.N. Lambrinos, G.D. Magoulas, A class of gradient unconstrained minimization algorithms with adaptive stepsize, J. Comput. Appl. Math. 114 (2000) 367--386.
Deterministic Nonmonotone Strategies for Effective.. - Plagianakos.. Self-citation (Vrahatis Magoulas) (Correct)
....[33] 38] Nevertheless, there are theoretical results that guarantee the convergence of batch BP algorithms for a constant learning rate. In this case, the learning rate should be proportional to the inverse of the Lipschitz constant which, in practice, is not easily available [2] 42] [69]. A variety of approaches adapted from numerical analysis have been applied, in an attempt to use second derivative related information to accelerate the learning process [6] 44] 46] 53] 68] 72] However, second order training algorithms are, in certain cases, computationally intensive ....
....neither the morphology of the error surface nor the value of the Lipschitz constant are known a priori. In order to alleviate this situation in [42] a local estimation of the Lipschitz constant has been proposed, which provides information related to the local shape of the error function (see also [69] for the usefulness of this estimate) The following procedure provides an elegant way to adapt the value of the nonmonotone learning horizon dynamically at the th iteration: otherwise (13) where is the local estimation of the Lipschitz constant at the th iteration [42] 14) which can be ....
M. N. Vrahatis, G. S. Androulakis, J. N. Lambrinos, and G. D. Magoulas, "A class of gradient unconstrained minimization algorithms with adaptive stepsize," J. Comput. Appl. Math., vol. 114, pp. 367--386, 2000.
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....maps two binary inputs to a single binary output and the network that was trained to solve the problem had two linear input nodes, two hidden nodes with logistic activations and one linear output node. Training the network corresponds to the minimization of a 9 dimensional objective function [5, 9]. It is well known from the neural networks literature that successful training in this case, i.e. reaching a global minimizer, strongly depends on the initial weight values and that the error function of the network presents a multitude of local minima. To solve this problem, we use the new ....
M.N. Vrahatis, G.S. Androulakis, J.N. Lambrinos and G.D. Magoulas, "A class of gradient unconstrained minimization algorithms with adaptive stepsize", J. of Comp. and App. Math., vol. 114, pp. 367--386, 2000.
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M. N. Vrahatis, G. S. Androulakis, J. N. Lambrinos, and G. D. Magoulas, "A class of gradient unconstrained minimization algorithms with adaptive stepsize," J. Comput. Appl. Math., vol. 114, pp. 367--386, 2000.
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M.N. Vrahatis, G.S. Androulakis, J.N. Lambrinos, G.D. Magoulas, A class of gradient unconstrained minimization algorithms with adaptive stepsize, J. Comp. Appl. Math. 114, 367-386, 2000.
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....but also indispensable. Moreover, in many applications there are imprecise values for the input data as well as for the function values. Therefore, the development of robust and efficient GO methods for dynamic environments such as the aforementioned, is a subject of considerable ongoing research [22]. Recently, Eberhart and Kennedy (1995) proposed the Particle Swarm Optimization (PSO) algorithm [9] a new, simple evolutionary algorithm, which differs from other evolution motivated evolutionary computation techniques in that it is motivated from the simulation of birds social behavior. ....
M.N. Vrahatis, G.S. Androulakis, J.N. Lambrinos, G.D. Magoulas, A class of gradient unconstrained minimization algorithms with adaptive stepsize, J. Comp. Appl. Math., 114, 2000, 367--386.
Stretching technique for obtaining global.. - Parsopoulos.. (2000) (1 citation) Self-citation (Vrahatis Magoulas) (Correct)
....problem. The XOR function maps two binary inputs to a single binary output and the ANN that was trained to solve the problem had 2 linear input nodes, two hidden nodes and one output node, all with logistic activations. This task corresponds to the minimization of the following objective function [13]: f(x) 1 exp ; x 7 1 exp( x 1 ; x 2 ; x 5 ) x 8 1 exp( x 3 ; x 4 ; x 6 ) x 9 ;2 1 exp ; x 7 1 exp( x 5 ) x 8 1 exp( x 6 ) x 9 ;2 1 ; ae 1 exp ; x 7 1 exp( x 1 ; x 5 ) x 8 1 exp( x 3 ; x 6 ) x 9 oe ;1 # 2 1 ....
M.N. Vrahatis, G.S. Androulakis, J.N. Lambrinos and G.D. Magoulas (2000), A class of gradientunconstrained minimization algorithms with adaptive stepsize. Journal of Computational and Applied Mathematics, 114, 367--386.
A Framework for the Development of Globally.. - Magoulas.. Self-citation (Vrahatis Androulakis Magoulas) (Correct)
....k # and (b) E(w k # m k 1 # k ) E(w k ) # m k 1 ###E(w k ) # k #. 5. Set w k 1 = w k # k # k . If k MIT , replace k by k 1, and go to Step 3; otherwise go to Step 6. 6. Output w k ; E(w k ) #E(w k ) For an extended version of Algorithm 1, see [26]. All the above strategies must be combined with tuning subprocedures generating learning rates that satisfy conditions (3) 4) or (6) 7) in order to guarantee global convergence. This issue is the subject of the next section. 4. Global convergence by tuning the learning rate In this section ....
....success with other popular training methods. The results have been quite satisfactory. Our experience is that these strategies behave predictably and reliably. In this section we report an instance of our experimental study. More specifically we exhibit results on the numeric font learning problem [14, 26] for the following methods: i) the batch Back Propagation (BP) with a constant learning rate [23] ii) the batch BP with adaptive learning rate [14] enhanced by the new strategy, which results in a BP training algorithm with inexact Line Search (BPLS) for the determination of a global learning ....
M.N. Vrahatis, G.S. Androulakis, J.N. Lambrinos and G.D. Magoulas, A class of gradient unconstrained minimization algorithms with adaptive stepsize, J. Comput. Appl. Math., 1999, accepted for publication.
From Linear to Nonlinear Iterative Methods - Vrahatis, al. (2003) (Correct)
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M.N. Vrahatis, G.S. Androulakis, J.N. Lambrinos, and G.D. Magoulas, A class of gradient unconstrained minimization algorithms with adaptive stepsize, J. Comput. Appl. Math.,vol. 114, pp.367-386, 2000.
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