Numerical Optimization: Mathematical Problems and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: closed (31 July 2020) | Viewed by 2008

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The High School of Cyberphysical Systems and Control, Institute of Computer Science and Technology, Peter the Great St. Petersburg Polytechnic University, 194021 Saint Petersburg, Russia
Interests: Applied Mathematics; Mathematical Physics; MATLAB Simulation; FPGA Accelerators; Nonlinear Dynamics; Advanced Control Theory; Fractional Calculus; Embedded Systems; Artificial Intelligence; Machine learning; System Modeling; Electrical & Electronics Engineering; Automation & Robotics; Human-Machine Interfaces; Mechatronics; Control and Instrumentation; Power Systems Modelling
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Special Issue Information

Dear Colleagues,

Almost every problem in science and technology can be formulated as an optimization problem. When solving these problems, computational methods based on mathematical analysis and natural calculations are used. At the same time, in practice, the problems of approximate solutions to optimization problems, the analysis of computational errors, and the convergence of computational methods come to the fore. In a number of complex problems, it is very difficult or impossible to obtain an analytical solution by means of mathematical analysis; therefore the issues of numerical algorithms are equally important. The purpose of this Special Issue is to establish a collection of articles that reflect the latest mathematical developments in the field of numerical optimization with their applications. The topics of this Special Issue include, but are not limited to:

  • Inverse and Incorrect Problems of Control Theory
  • Problems of Perturbation of the Spectrum of Operators in the Theory of Dynamical Systems
  • Simulation-based optimization
  • Nonlinear ODEs and PDEs
  • Applied Mathematical Modelling in Fluid and Solid Mechanics
  • Analytical Approximate Methods
  • Fractional Calculus

Dr. Anton Zhilenkov
Guest Editor

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Keywords

  • Inverse and ill-posed problems
  • Perturbation of the spectrum of operators
  • Predictor–corrector method
  • Simulation-based optimization
  • Numerical algorithms
  • Convergence analysis
  • Nonsmooth optimization
  • Near-optimal solution

Published Papers (1 paper)

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Research

20 pages, 844 KiB  
Article
Empirical Means on Pseudo-Orthogonal Groups
by Jing Wang, Huafei Sun and Simone Fiori
Mathematics 2019, 7(10), 940; https://doi.org/10.3390/math7100940 - 11 Oct 2019
Cited by 2 | Viewed by 2338
Abstract
The present article studies the problem of computing empirical means on pseudo-orthogonal groups. To design numerical algorithms to compute empirical means, the pseudo-orthogonal group is endowed with a pseudo-Riemannian metric that affords the computation of the exponential map in closed forms. The distance [...] Read more.
The present article studies the problem of computing empirical means on pseudo-orthogonal groups. To design numerical algorithms to compute empirical means, the pseudo-orthogonal group is endowed with a pseudo-Riemannian metric that affords the computation of the exponential map in closed forms. The distance between two pseudo-orthogonal matrices, which is an essential ingredient, is computed by both the Frobenius norm and the geodesic distance. The empirical-mean computation problem is solved via a pseudo-Riemannian-gradient-stepping algorithm. Several numerical tests are conducted to illustrate the numerical behavior of the devised algorithm. Full article
(This article belongs to the Special Issue Numerical Optimization: Mathematical Problems and Applications)
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