Prof. Delfim Torres: New Applications
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en-us2022 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSun, 23 Jan 2022 15:04:37 GMTSun, 23 Jan 2022 15:04:37 GMTNew applications published by Prof. Delfim Torreshttps://www.maplesoft.com/images/Application_center_hp.jpgProf. Delfim Torres: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=17417
A Computational Approach to Essential and Nonessential Objective Functions in Linear Multicriteria Optimization
https://www.maplesoft.com/applications/view.aspx?SID=7061&ref=Feed
<strong>Authors</strong>: Prof. Agnieszka B. Malinowska and Prof. Delfim F. M. Torres
The question of obtaining well-defined criteria for multiple criteria decision making problems is well-known. One of the approaches dealing with this question is the concept of nonessential objective function. A certain objective function is called nonessential if the set of efficient solutions is the same both with or without that objective function. In this work we put together two methods for determining nonessential objective functions. A computational implementation is done using the computer algebra system Maple.<img src="https://www.maplesoft.com/view.aspx?si=7061/1.jpg" alt="A Computational Approach to Essential and Nonessential Objective Functions in Linear Multicriteria Optimization" style="max-width: 25%;" align="left"/><strong>Authors</strong>: Prof. Agnieszka B. Malinowska and Prof. Delfim F. M. Torres
The question of obtaining well-defined criteria for multiple criteria decision making problems is well-known. One of the approaches dealing with this question is the concept of nonessential objective function. A certain objective function is called nonessential if the set of efficient solutions is the same both with or without that objective function. In this work we put together two methods for determining nonessential objective functions. A computational implementation is done using the computer algebra system Maple.https://www.maplesoft.com/applications/view.aspx?SID=7061&ref=FeedTue, 23 Dec 2008 00:00:00 ZProf. Delfim TorresProf. Delfim TorresComputing ODE symmetries as abnormal variational symmetries
https://www.maplesoft.com/applications/view.aspx?SID=6881&ref=Feed
We give a new computational method to obtain symmetries of ordinary differential equations. The proposed approach appears as an extension of a recent algorithm to compute variational symmetries of optimal control problems [P.D.F. Gouveia, D.F.M. Torres, Automatic computation of conservation laws in the calculus of variations and optimal control, Comput. Methods Appl. Math. 5 (4) (2005) 387-409], and is based on the resolution of a first order linear PDE that arises as a necessary and sufficient condition of invariance for abnormal optimal control problems. A computer algebra procedure is developed, which permits one to obtain ODE symmetries by the proposed method. Examples are given, and results compared with those obtained by previous available methods.<img src="https://www.maplesoft.com/view.aspx?si=6881/1.jpg" alt="Computing ODE symmetries as abnormal variational symmetries" style="max-width: 25%;" align="left"/>We give a new computational method to obtain symmetries of ordinary differential equations. The proposed approach appears as an extension of a recent algorithm to compute variational symmetries of optimal control problems [P.D.F. Gouveia, D.F.M. Torres, Automatic computation of conservation laws in the calculus of variations and optimal control, Comput. Methods Appl. Math. 5 (4) (2005) 387-409], and is based on the resolution of a first order linear PDE that arises as a necessary and sufficient condition of invariance for abnormal optimal control problems. A computer algebra procedure is developed, which permits one to obtain ODE symmetries by the proposed method. Examples are given, and results compared with those obtained by previous available methods.https://www.maplesoft.com/applications/view.aspx?SID=6881&ref=FeedTue, 11 Nov 2008 00:00:00 ZProf. Delfim TorresProf. Delfim TorresAutomatic Computation of Conservation Laws in the Calculus of Variations and Optimal Control
https://www.maplesoft.com/applications/view.aspx?SID=4805&ref=Feed
We present analytic computational tools that permit us to identify, in an automatic way, conservation laws in optimal control. The central result we use is the famous Noetherâ€™s theorem, a classical theory developed by Emmy Noether in 1918, in the context of the calculus of variations and mathematical physics, and which was extended recently to the more general context of optimal control. We show how a Computer Algebra System can be very helpful in finding the symmetries and corresponding conservation laws in optimal control theory, thus making useful in practice the theoretical results recently obtained in the literature. A Maple implementation is provided and several illustrative examples given.<img src="https://www.maplesoft.com/view.aspx?si=4805/gouveia-torres-CLsOptCont_5.gif" alt="Automatic Computation of Conservation Laws in the Calculus of Variations and Optimal Control" style="max-width: 25%;" align="left"/>We present analytic computational tools that permit us to identify, in an automatic way, conservation laws in optimal control. The central result we use is the famous Noetherâ€™s theorem, a classical theory developed by Emmy Noether in 1918, in the context of the calculus of variations and mathematical physics, and which was extended recently to the more general context of optimal control. We show how a Computer Algebra System can be very helpful in finding the symmetries and corresponding conservation laws in optimal control theory, thus making useful in practice the theoretical results recently obtained in the literature. A Maple implementation is provided and several illustrative examples given.https://www.maplesoft.com/applications/view.aspx?SID=4805&ref=FeedWed, 26 Jul 2006 00:00:00 ZProf. Delfim TorresProf. Delfim Torres