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Mathematics
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Optimization Methods in Engineering Mathematics
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Optimization Methods in Engineering Mathematics

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 20 June 2025 | Viewed by 2952

Special Issue Editors

Dr. Houari Mechkour

E-Mail Website
Guest Editor
ECE-Paris Engineering School, 37 Quai de Grenelle, CS-71520, CEDEX 15, 75015 Paris, France
Interests: financial engineering mathematics; shape optimization
Prof. Dr. Mohammed Louaked

E-Mail Website
Guest Editor
Laboratoire de Mathématiques Nicolas Oresme, Université de Caen, 14000 Caen, France
Interests: numerical analysis methods; computational mathematics engineering; applied and computational mathematics; water quality; multiphase flow modeling

Special Issue Information

Dear Colleagues,

We are pleased to announce the launch of a Special Issue on the important scientific topic of “Optimization Methods in Engineering Mathematics” for Mathematics. This Special Issue aims to explore the most recent developments in the application of control and optimization techniques, and covers a broad area of research activities in control, modeling, analysis, and optimization: optimization in energy, control of PDEs, computational mathematics for control and optimization, data assimilation, control techniques for financial mathematics, optimization in health care, and control of biological systems.

Dr. Houari Mechkour
Prof. Dr. Mohammed Louaked
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • optimization in science and engineering
  • PDE-constrained optimization
  • optimization algorithms and solution techniques
  • analysis and control of nonlinear systems
  • data assimilation
  • industrial applications

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Published Papers (2 papers)

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Research

33 pages, 1650 KiB  
Article
Approximate Closed-Form Solutions for Pricing Zero-Coupon Bonds in the Zero Lower Bound Framework
by Jae-Yun Jun and Yves Rakotondratsimba
Mathematics 2024, 12(17), 2690; https://doi.org/10.3390/math12172690 - 29 Aug 2024
Viewed by 742
Abstract
After the 2007 financial crisis, many central banks adopted policies to lower their interest rates; the dynamics of these rates cannot be captured using classical models. Recently, Meucci and Loregian proposed an approach to estimate nonnegative interest rates using the inverse-call transformation. Despite [...] Read more.
After the 2007 financial crisis, many central banks adopted policies to lower their interest rates; the dynamics of these rates cannot be captured using classical models. Recently, Meucci and Loregian proposed an approach to estimate nonnegative interest rates using the inverse-call transformation. Despite the fact that their work is distinguished from others in the literature by their consideration of practical aspects, some technical difficulties still remain, such as the lack of analytic expression for the zero-coupon bond (ZCB) price. In this work, we propose novel approximate closed-form solutions for the ZCB price in the zero lower bound (ZLB) framework, when the underlying shadow rate is assumed to follow the classical one-factor Vasicek model. Then, a filtering procedure is performed using the Unscented Kalman Filter (UKF) to estimate the unobservable state variable (the shadow rate), and the model calibration is proceeded by estimating the model parameters using the Particle Swarm Optimization (PSO) algorithm. Further, empirical illustrations are given and discussed using (as input data) the interest rates of the AAA-rated bonds compiled by the European Central Bank ranging from 6 September 2004 to 21 June 2012 (a period that concerns the ZLB framework). Our approximate closed-form solution is able to show a good match between the actual and estimated yield-rate values for short and medium time-to-maturity values, whereas, for long time-to-maturity values, it is able to estimate the trend of the yield rates. Full article
(This article belongs to the Special Issue Optimization Methods in Engineering Mathematics)
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17 pages, 4502 KiB  
Article
Optimal Control Strategies for Mitigating Urban Heat Island Intensity in Porous Urban Environments
by Nacer Sellila, Mohammed Louaked, Waleed Mouhali and Houari Mechkour
Mathematics 2023, 11(23), 4737; https://doi.org/10.3390/math11234737 - 23 Nov 2023
Viewed by 1562
Abstract
This work is intended as an attempt to explore the use of optimal control techniques for designing green spaces and for dealing with the environmental problems related to urban heat islands appearing in cities. A three-dimensional model is established for numerical studies of [...] Read more.
This work is intended as an attempt to explore the use of optimal control techniques for designing green spaces and for dealing with the environmental problems related to urban heat islands appearing in cities. A three-dimensional model is established for numerical studies of the effects of urban anthropogenic heat and wind velocity in urban and rural regions. The transport mechanism of fluid in the cities is governed by the Navier–Stokes–Forschheimer porous media system. We introduce the penalty approximation method to overcome the difficulty induced by the incompressibility constraint. The partial differential equation optimal control problem is solved by using a Spectral Projected Gradient algorithm. To validate the method, we implement a numerical scheme, based on a finite element method, employing the free software FreeFem++ 14.3. We show the results for the optimized and non-optimized situations to compare the two cases. Full article
(This article belongs to the Special Issue Optimization Methods in Engineering Mathematics)
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