1,720,974 research outputs found
Neural networks, surrogate models and black box algorithms: theory and applications
Full text linkIn this Ph. D. Thesis we will analyze some of the most used surrogate models,
together with a particular type of line search black box strategy. After introducing
these powerful tools, we will present the Canonical Duality Theory, the potentiality
it has to improve these tools, and some of their applications.
The principal contributes of this Thesis are the reformulation of the Radial Basis
Neural Network problem in its canonical dual form in Section 2.2 and the application
of the surrogate models and black box algorithms presented in this Thesis on various
real world problems reported in Chapter 3
Canonical duality for solving general nonconvex constrained problems
No full textThis paper presents a canonical duality theory for solving a general nonconvex constrained optimization problem within a unified framework
to cover Lagrange multiplier method and KKT theory.
It is proved that if both target function and constraints possess certain patterns necessary for modeling real systems,
a perfect dual problem (without duality gap)
can be obtained in a unified form with global optimality conditions provided.
While the popular augmented Lagrangian method may produce more difficult nonconvex problems due to the nonlinearity of constraints
Canonical dual solutions to nonconvex radial basis neural network optimization problem
No full textRadial Basis Functions Neural Networks (RBFNNs) are tools widely used in regression problems. One of their principal drawbacks is that the formulation corresponding to the training with the supervision of both the centers and the weights is a highly non-convex optimization problem, which leads to some fundamental difficulties for the traditional optimization theory and methods. This paper presents a generalized canonical duality theory for solving this challenging problem. We demonstrate that by using sequential canonical dual transformations, the nonconvex optimization problem of the RBFNN can be reformulated as a canonical dual problem (without duality gap). Both global optimal solution and local extrema can be classified. Several applications to one of the most used Radial Basis Functions, the Gaussian function, are illustrated. Our results show that even for a one-dimensional case, the global minimizer of the nonconvex problem may not be the best solution to the RBFNNs, and the canonical dual theory is a promising tool for solving general neural networks training problems. © 2014 Elsevier B.V.Radial Basis Functions Neural Networks (RBFNNs) are tools widely used in regression problems. One of their principal drawbacks is that the formulation corresponding to the training with the supervision of both the centers and the weights is a highly non-convex optimization problem, which leads to some fundamentally difficulties for
traditional optimization theory and methods.
This paper presents a generalized canonical duality theory for solving this
challenging problem. We demonstrate that by using sequential canonical dual transformations, the
nonconvex optimization problem of the RBFNN can be reformulated as a canonical dual problem (without duality gap).
Both global optimal solution and local extrema can be classified.
Several applications to one of the most used Radial Basis Functions, the Gaussian function, are illustrated.
Our results show that even for one-dimensional case, the global minimizer of the nonconvex problem
may not be the best solution to the RBFNNs
Canonical Duality-Triality Theory: Bridge Between Nonconvex Analysis/Mechanics and Global Optimization in Complex Systems
No full textCanonical duality-triality is a breakthrough
methodological theory, which can be used not only for modeling complex systems within
a unified framework, but also for solving a wide class of challenging problems from real-world applications.
This paper presents a brief review on this theory, its philosophical origin, physics foundation, and
mathematical statements in both finite and infinite dimensional spaces.
Particular emphasis is placed on its
role for bridging the gap between nonconvex analysis/mechanics and global optimization.
Special attentions are paid on unified
understanding the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science,
and the NP-hard problems in global optimization,
as well as the theorems, methods, and algorithms for solving these challenging problems
Support vector machines for surrogate modeling of electronic circuits
No full textIn electronic circuit design, preliminary analyses of the circuit performances are generally carried out using time-consuming simulations. These analyses should be performed as fast as possible because of the strict temporal constraints on the industrial sector time to market. On the other hand, there is the need of precision and reliability of the analyses. For these reasons, there is more and more interest toward surrogate models able to approximate the behavior of a device with a high precision making use of a limited set of samples. Using suitable surrogate models instead of simulations, it is possible to perform a reliable analysis in less time. In this work, we are going to analyze how the surrogate models given by the support vector machine (SVM) perform when they are used to approximate the behavior of industrial circuits that will be employed in consumer electronics. The SVM is also compared to the surrogate models given by the response surface methodology using a commercial software currently adopted for this kind of applications
A canonical duality approach for the solution of affine quasi-variational inequalities
No full textWe apply a sequential dual canonical transformation on the global optimization problem resulting from the reformulation of the Karush–Kuhn– Tucker conditions of affine quasi-variational inequalities (QVIs) using the Fischer- Burmeister complementarity function. Canonical duality is generally able to provide conditions for a critical point of the dual formulation to be the corresponding point of a global optimum of the original problem. By studying the new dual formulation it is possible to obtain properties that are not evident from the original one and that can be useful to develop new methods for the solution of (not necessarily affine) QVIs. The resulting formulation is canonically dual to the original in the sense that there is no duality gap between critical points of the original problem and those of the dual one
Canonical Duality for Radial Basis Neural Networks
No full textRadial Basis Function Neural Networks (RBF NN) are a tool largely used for regression problems. The principal drawback of this kind of predictive tool is that the optimization problem solved to train the network can be non-convex. On the other hand Canonical Duality Theory offers a powerful procedure to reformulate general non-convex problems in dual forms so that it is possible to find optimal solutions and to get deep insights into the nature of the challenging problems. By combining the canonical duality theory with the RBF NN, this paper presents a potentially useful method for solving challenging problems in real-world applications. © Springer-Verlag Berlin Heidelberg 2013.Radial Basis Function Neural Networks(RBF NN) are a tool largely used for regression problems. The principal drawback of this kind of predictive tool is that the optimization problem solved to train the network can be non-convex. On the other hand Canonical Duality Theory offers a powerful procedure to reformulate general non-convex problems in dual forms so that it is possible to find optimal solutions and to get deep insights into the nature of the challenging problems. By combining the canonical duality theory with the RBF NN, this paper presents a potentially useful method for solving challenging problems in real-world applications
Derivative free methodologies for circuit worst case analysis
No full textIn this paper, a new derivative-free method for Worst Case Analysis (WCA) of circuit design is defined. A WCA of a device can be performed by solving a particular minimization problem where the objective function values are obtained by a simulation code and where some variables are subject to a spherical constraint and others to box constraints. In order to efficiently tackle such a problem, the paper defines a new DF algorithm which follows a two blocks Gauss Seidel approach, namely it alternates an approximated minimization with respect to the variables subject to the spherical constraint with an approximated minimization respect to the variables subject to the box constraints. The algorithm is described and its global convergence properties are analyzed. Furthermore it is tested in the WCA of a MOSFET operational amplifier and its computational behaviour is compared with the one of the efficient optimization tool of the WiCkeD suite for circuit analysis. The obtained results seem to indicate that the proposed algorithm is promising in terms of average efficiency, accuracy and robustness
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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