27 research outputs found
Qualification Conditions for Calculus Rules of Coderivatives of Multivalued Mappings
AbstractThis paper establishes by a general approach a full calculus for the limiting Fréchet and the approximate coderivatives of multivalued mappings. This approach allows us to produce several new verifiable qualification conditions for such calculus rules
Master index
Pla general, del mural cerĂ mic que decora una de les parets del vestĂbul de la Facultat de QuĂmica de la UB. El mural representa diversos sĂmbols relacionats amb la quĂmica
Universal Approximation of Parametric Optimization via Neural Networks with Piecewise Linear Policy Approximation
Parametric optimization solves a family of optimization problems as a
function of parameters. It is a critical component in situations where optimal
decision making is repeatedly performed for updated parameter values, but
computation becomes challenging when complex problems need to be solved in
real-time. Therefore, in this study, we present theoretical foundations on
approximating optimal policy of parametric optimization problem through Neural
Networks and derive conditions that allow the Universal Approximation Theorem
to be applied to parametric optimization problems by constructing piecewise
linear policy approximation explicitly. This study fills the gap on formally
analyzing the constructed piecewise linear approximation in terms of
feasibility and optimality and show that Neural Networks (with ReLU
activations) can be valid approximator for this approximation in terms of
generalization and approximation error. Furthermore, based on theoretical
results, we propose a strategy to improve feasibility of approximated solution
and discuss training with suboptimal solutions.Comment: 17 pages, 2 figures, preprint, under revie
The Encyclopedia of Neutrosophic Researchers - vol. 1
This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements
Fractional Calculus - Theory and Applications
In recent years, fractional calculus has led to tremendous progress in various areas of science and mathematics. New definitions of fractional derivatives and integrals have been uncovered, extending their classical definitions in various ways. Moreover, rigorous analysis of the functional properties of these new definitions has been an active area of research in mathematical analysis. Systems considering differential equations with fractional-order operators have been investigated thoroughly from analytical and numerical points of view, and potential applications have been proposed for use in sciences and in technology. The purpose of this Special Issue is to serve as a specialized forum for the dissemination of recent progress in the theory of fractional calculus and its potential applications
Nondifferentiable Optimization: Motivations and Applications
IIASA has been involved in research on nondifferentiable optimization since 1976. The Institute's research in this field has been very productive, leading to many important theoretical, algorithmic and applied results. Nondifferentiable optimization has now become a recognized and rapidly developing branch of mathematical programming. To continue this tradition and to review developments in this field IIASA held this Workshop in Sopron (Hungary) in September 1984.
This volume contains selected papers presented at the Workshop. It is divided into four sections dealing with the following topics: (I) Concepts in Nonsmooth Analysis; (II) Multicriteria Optimization and Control Theory; (III) Algorithms and Optimization Methods; (IV) Stochastic Programming and Applications