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- M. S. Apostolopoulou, D. G. Sotiropoulos, Panayiotis E. Pintelas
- Optimization Methods and Software
- 2008

We present a new matrix-free method for the large-scale trust-region subproblem, assuming that the approximate Hessian is updated by the L-BFGS formula with m = 1 or 2. We determine via simple formulas the eigenvalues of these matrices and, at each iteration, we construct a positive definite matrix whose inverse can be expressed analytically, without using… (More)

In this work, an efficient training algorithm for feedforward neural networks is presented. It is based on a scaled version of the conjugate gradient method suggested by Perry, which employs the spectral steplength of Barzilai and Borwein that contains second order information without estimating the Hessian matrix. The learning rate is automatically adapted… (More)

Methods of interval arithmetic can be used to reliably find with certainty all solutions to nonlinear systems of equations. In such methods, the system is transformed into a linear interval system and a preconditioned interval Gauss-Seidel method may then be used to compute such solution bounds. In this work, a new heuristic for solving polynomial systems… (More)

We present an interval algorithm for solving discrete minimax problems where the constituent minimax functions are continuously differentiable functions of one real variable. Our approach is based on smoothing the max-type function by exploiting the Jaynes’s maximum entropy [Phys. Rev., 106:620–630, 1957]. The algorithm works within the branchand-bound… (More)

- Ioannis E. Livieris, M. S. Apostolopoulou, D. G. Sotiropoulos, Spyros Sioutas, Panayiotis E. Pintelas
- 2009 13th Panhellenic Conference on Informatics
- 2009

Artificial neural networks have been widely used for knowledge extraction from biomedical datasets and constitute an important role in bio-data exploration and analysis.In this work, we proposed a new curvilinear algorithm for training large neural networks which is based on the analysis of the eigenstructure of the memoryless BFGS matrices. The proposed… (More)

We present a branch-and-prune algorithm for univariate optimization. Pruning is achieved by using first order information of the objective function by means of an interval evaluation of the derivative over the current interval. First order information aids fourfold. Firstly, to check monotonicity. Secondly, to determine optimal centers which, along with the… (More)

A new evolutionary algorithm for the global optimization of multimodal functions is presented. The algorithm is essentially a parallel direct search method which maintains a populations of individuals and utilizes an evolution operator to evolve them. This operator has two functions. Firstly, to exploit the search space as much as possible, and secondly to… (More)

We present a new method for computing verified enclosures for the global minimum value and all global minimum points of univariate functions subject to bound constrains. The method works within the branch and bound framework and incorporates inner and outer pruning steps by using first order information of the objective function by means of an interval… (More)

- D. G. Sotiropoulos, Theodoula N. Grapsa
- Applied Mathematics and Computation
- 2005

We present an interval branch-and-prune algorithm for computing verified enclosures for the global minimum and all global minimizers of univariate functions subject to bound constraints. The algorithm works within the branch-and-bound framework and uses first order information of the objective function. In this context, we investigate valuable properties of… (More)

- M. S. Apostolopoulou, D. G. Sotiropoulos, C. A. Botsaris
- Applied Mathematics and Computation
- 2010

We present a newmatrix-free method for the computation of negative curvature directions based on the eigenstructure of minimal-memory BFGS matrices. We determine via simple formulas the eigenvalues of these matrices and we compute the desirable eigenvectors by explicit forms. Consequently, a negative curvature direction is computed in such a way that avoids… (More)