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Academic literature on the topic 'Variational problem'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "Variational problem"

1

Palese, Marcella. "Variations by generalized symmetries of local Noether strong currents equivalent to global canonical Noether currents." Communications in Mathematics 24, no. 2 (December 1, 2016): 125–35. http://dx.doi.org/10.1515/cm-2016-0009.

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Abstract We will pose the inverse problem question within the Krupka variational sequence framework. In particular, the interplay of inverse problems with symmetry and invariance properties will be exploited considering that the cohomology class of the variational Lie derivative of an equivalence class of forms, closed in the variational sequence, is trivial. We will focalize on the case of symmetries of globally defined field equations which are only locally variational and prove that variations of local Noether strong currents are variationally equivalent to global canonical Noether currents. Variations, taken to be generalized symmetries and also belonging to the kernel of the second variational derivative of the local problem, generate canonical Noether currents - associated with variations of local Lagrangians - which in particular turn out to be conserved along any section. We also characterize the variation of the canonical Noether currents associated with a local variational problem.

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Hua, Yuan, Bao Hua Lv, and Tai Quan Zhou. "Parametric Variational Principle for Solving Coupled Damage Problem." Key Engineering Materials 348-349 (September 2007): 813–16. http://dx.doi.org/10.4028/www.scientific.net/kem.348-349.813.

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The parametric variational principle adopts the extreme variational idea in the modern control theory and uses state equations deduced from the constitutive law to control the functional variation, which is an effective solution to the nonlinear equations. Based on the fundamental equations of elasto-plasticity coupled damage problem, the potential functional of elasto-plasticity is constructed. Also the state equations with approximation of damage evolution equation and load functions are constructed in the paper. The solution of elasto-plasticity damage problem can be deduced to solve problem of the minimum potential energy function under the restriction of state equations. Thus the parametric variational principle for coupled damage is proposed. The variational principle has the virtue of definite physical meaning and the finite element equations are presented in the article to facilitate the application of parametric variatioal principle, which is easy to program on computer. Using the method mentioned in the article, a numerical calculation is carried out and the calculation result shows that the method is efficient for solving elasto-plasticity damage problem.

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Garg, Anupam. "Two variational variations on a problem in electrostatics." American Journal of Physics 75, no. 6 (June 2007): 509–12. http://dx.doi.org/10.1119/1.2717220.

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Zorii, N. V. "Extremal problems dual to the Gauss variational problem." Ukrainian Mathematical Journal 58, no. 6 (June 2006): 842–61. http://dx.doi.org/10.1007/s11253-006-0108-3.

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Bistafa, Sylvio R. "Euler's Navigation Variational Problem." Euleriana 2, no. 2 (September 19, 2022): 131. http://dx.doi.org/10.56031/2693-9908.1045.

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Onofri, E. "A Nonlinear Variational Problem." SIAM Review 27, no. 4 (December 1985): 576–78. http://dx.doi.org/10.1137/1027155.

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Cruz, Fátima, Ricardo Almeida, and Natália Martins. "Herglotz Variational Problems Involving Distributed-Order Fractional Derivatives with Arbitrary Smooth Kernels." Fractal and Fractional 6, no. 12 (December 10, 2022): 731. http://dx.doi.org/10.3390/fractalfract6120731.

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In this paper, we consider Herglotz-type variational problems dealing with fractional derivatives of distributed-order with respect to another function. We prove necessary optimality conditions for the Herglotz fractional variational problem with and without time delay, with higher-order derivatives, and with several independent variables. Since the Herglotz-type variational problem is a generalization of the classical variational problem, our main results generalize several results from the fractional calculus of variations. To illustrate the theoretical developments included in this paper, we provide some examples.

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Parida, J., M. Sahoo, and A. Kumar. "A variational-like inequality problem." Bulletin of the Australian Mathematical Society 39, no. 2 (April 1989): 225–31. http://dx.doi.org/10.1017/s0004972700002690.

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Given a closed and convex set K in Rn and two continuous maps F: K → Rn and η: K × K → Rn, the problem considered here is to find ε K such that.We call it a variational-like inequality problem, and develop a theory for the existence of a solution. We also show the relationship between the variational-like inequality problem and some mathematical programming problems.

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Jha, Shalini, Prasun Das, and Tadeusz Antczak. "Exponential type duality for η-approximated variational problems." Yugoslav Journal of Operations Research 30, no. 1 (2020): 19–43. http://dx.doi.org/10.2298/yjor190415022j.

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In this article, we use the so-called ?-approximation method for solving a new class of nonconvex variational problems with exponential (p, r)-invex functionals. In this approach, we construct ?-approximated variational problem and ?-approximated Mond- Weir dual variational problem for the considered variational problem and its Mond-Weir dual variational problem. Then several duality results for considered variational problem and its Mond-Weir dual variational problem are proved by the help of duality results established between ?-approximated variational problems mentioned above.

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Bock, Igor, and Ján Lovíšek. "An optimal control problem for a pseudoparabolic variational inequality." Applications of Mathematics 37, no. 1 (1992): 62–80. http://dx.doi.org/10.21136/am.1992.104492.

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Dissertations / Theses on the topic "Variational problem"

1

Brading, Katherine. "Symmetries, conservation laws and Noether's variational problem." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.288912.

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Arceci, Francesca. "Variational algorithms for image Super Resolution." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19509/.

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La Super Resolution è una tecnica che permette di aumentare la risoluzione di un’immagine oltre i limiti imposti dai sensori. Nel processo di acquisizione e formazione dell’immagine, vi sono infatti fenomeni di noise e blurring che la corrompono: da qui l’esigenza di ricostruire l’input reale. Una volta modellizzato questo processo, vi sono svariate tecniche SR che approcciano in modi differenti al problema: in questo lavoro ci basiamo su teniche reconstruction-based che prevedono la minimizzazione di due funzionali, uno che misura la coerenza tra dato e soluzione, l’altro è un termine di regolarizzazione. Lo studio di questa tesi si basa su un’immagine con gradiente sparso, più precisamente un QR code: partendo dalla descrizione del modello matematico, il nostro lavoro sarà quello di trovare un funzionale di regolarizzazione che esprima la proprietà del gradiente sparso e, basandoci sull’approccio dell’ Alternating Direction Method of Multipliers, implementare un nuovo algoritmo che risolva il problema di minimo ad esso associato. Mostreremo i risultati ottenuti confrontandoli con algoritmi preesistenti per provarne la buona performance.

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Haben, Stephen A. "Conditioning and preconditioning of the minimisation problem in variational data assimilation." Thesis, University of Reading, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.541945.

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Chi, Xuguang. "A non-variational approach to the quantum three-body coulomb problem /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202004%20CHI.

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Fiscella, A. "VARIATIONAL PROBLEMS INVOLVING NON-LOCAL ELLIPTIC OPERATORS." Doctoral thesis, Università degli Studi di Milano, 2014. http://hdl.handle.net/2434/245334.

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My thesis deals with nonlinear elliptic problems involving a non-local integrodifferential operator of fractional type. Our main results concern the existence of weak solutions for these problems and they are obtained using variational and topological methods.

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Salavessa, Isabel. "Graphs with parallel mean curvature and a variational problem in conformal geometry." Thesis, University of Warwick, 1987. http://wrap.warwick.ac.uk/99902/.

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This thesis essentially deals with two basic problems, one in Rieinannian, the other in Conformal Geometry, described in Part I resp. Part III. Part II can be considered as an interlude serving as a sort of bridge between Riemannian and Comformal Geometry.

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Agnihotri, Mayank P. "One particle properties in the 2D Coulomb problem Luttinger-Ward variational approach /." kostenfrei, 2007. http://www.digibib.tu-bs.de/?docid=00020957.

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Köhler, Karoline Sophie. "On efficient a posteriori error analysis for variational inequalities." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17635.

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Effiziente und zuverlässige a posteriori Fehlerabschätzungen sind eine Hauptzutat für die effiziente numerische Berechnung von Lösungen zu Variationsungleichungen durch die Finite-Elemente-Methode. Die vorliegende Arbeit untersucht zuverlässige und effiziente Fehlerabschätzungen für beliebige Finite-Elemente-Methoden und drei Variationsungleichungen, nämlich dem Hindernisproblem, dem Signorini Problem und dem Bingham Problem in zwei Raumdimensionen. Die Fehlerabschätzungen hängen vom zum Problem gehörenden Lagrange Multiplikator ab, der eine Verbindung zwischen der Variationsungleichung und dem zugehörigen linearen Problem darstellt. Effizienz und Zuverlässigkeit werden bezüglich eines totalen Fehlers gezeigt. Die Fehleranschätzungen fordern minimale Regularität. Die Approximation der exakten Lösung erfüllt die Dirichlet Randbedingungen und die Approximation des Lagrange Multiplikators ist nicht-positiv im Falle des Hindernis- und Signoriniproblems, und hat Betrag kleiner gleich 1 für das Bingham Problem. Dieses allgemeine Vorgehen ermöglicht das Einbinden nicht-exakter diskreter Lösungen, welche im Kontext dieser Ungleichungen auftreten. Aus dem Blickwinkel der Anwendungen ist Effizienz und Zuverlässigkeit im Bezug auf den Fehler der primalen Variablen in der Energienorm von großem Interesse. Solche Abschätzungen hängen von der Wahl eines effizienten diskreten Lagrange Multiplikators ab. Im Falle des Hindernis- und Signorini Problems werden postive Beispiele für drei Finite-Elemente Methoden, der konformen Courant Methode, der nicht-konformen Crouzeix-Raviart Methode und der gemischten Raviart-Thomas Methode niedrigster Ordnung hergeleitet. Partielle Resultate liegen im Fall des Bingham Problems vor. Numerischer Experimente heben die theoretischen Ergebnisse hervor und zeigen Effizienz und Zuverlässigkeit. Die numerischen Tests legen nahe, dass der aus den Abschätzungen resultierende adaptive Algorithmus mit optimaler Konvergenzrate konvergiert.
Efficient and reliable a posteriori error estimates are a key ingredient for the efficient numerical computation of solutions for variational inequalities by the finite element method. This thesis studies such reliable and efficient error estimates for arbitrary finite element methods and three representative variational inequalities, namely the obstacle problem, the Signorini problem, and the Bingham problem in two space dimensions. The error estimates rely on a problem connected Lagrange multiplier, which presents a connection between the variational inequality and the corresponding linear problem. Reliability and efficiency are shown with respect to some total error. Reliability and efficiency are shown under minimal regularity assumptions. The approximation to the exact solution satisfies the Dirichlet boundary conditions, and an approximation of the Lagrange multiplier is non-positive in the case of the obstacle and Signorini problem and has an absolute value smaller than 1 for the Bingham flow problem. These general assumptions allow for reliable and efficient a posteriori error analysis even in the presence of inexact solve, which naturally occurs in the context of variational inequalities. From the point of view of the applications, reliability and efficiency with respect to the error of the primal variable in the energy norm is of great interest. Such estimates depend on the efficient design of a discrete Lagrange multiplier. Affirmative examples of discrete Lagrange multipliers are presented for the obstacle and Signorini problem and three different first-order finite element methods, namely the conforming Courant, the non-conforming Crouzeix-Raviart, and the mixed Raviart-Thomas FEM. Partial results exist for the Bingham flow problem. Numerical experiments highlight the theoretical results, and show efficiency and reliability. The numerical tests suggest that the resulting adaptive algorithms converge with optimal convergence rates.

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El-Said, Adam. "Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction." Thesis, University of Reading, 2015. http://centaur.reading.ac.uk/45568/.

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4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

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Vedovato, Mattia. "Some variational and geometric problems on metric measure spaces." Doctoral thesis, Università degli studi di Trento, 2022. https://hdl.handle.net/11572/337379.

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In this Thesis, we analyze three variational and geometric problems, that extend classical Euclidean issues of the calculus of variations to more general classes of spaces. The results we outline are based on the articles [Ved21; MV21] and on a forthcoming joint work with Nicolussi Golo and Serra Cassano. In the first place, in Chapter 1 we provide a general introduction to metric measure spaces and some of their properties. In Chapter 2 we extend the classical Talenti’s comparison theorem for elliptic equations to the setting of RCD(K,N) spaces: in addition the the generalization of Talenti’s inequality, we will prove that the result is rigid, in the sense that equality forces the space to have a symmetric structure, and stable. Chapter 3 is devoted to the study of the Bernstein problem for intrinsic graphs in the first Heisenberg group H^1: we will show that under mild assumptions on the regularity any stationary and stable solution to the minimal surface equation needs to be intrinsically affine. Finally, in Chapter 4 we study the dimension and structure of the singular set for p-harmonic maps taking values in a Riemannian manifold.

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Books on the topic "Variational problem"

1

The inverse variational problem in classical mechanics. Singapore: World Scientific Pub. Co., 1999.

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Jong-Shi, Pang, ed. Finite-dimensional variational inequalities and complementarity problems. New York: Springer, 2003.

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C, Ferris Michael, Pang Jong-Shi, and International Conference on Complementarity Problems (1995 : Baltimore, Md.), eds. Complementarity and variational problems: State of the art. Philadelphia: Society for Industrial and Applied Mathematics, 1997.

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Zaslavski, Alexander J. Structure of Solutions of Variational Problems. New York, NY: Springer New York, 2013.

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Kassay, Gábor. The equilibrium problem and related topics. Cluj-Napoca: Risoprint, 2000.

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1963-, Varga Kálmán, ed. Stochastic variational approach to quantum-mechanical few-body problems. Berlin: Springer, 1998.

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1952-, Kunisch K., ed. Lagrange multiplier approach to variational problems and applications. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2008.

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Salavessa, Isabel Maria da Costa. Graphs with parallel mean curvature and a variational problem in conformal geometry. [s.l.]: typescript, 1987.

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Mawhin, J. Problèmes de Dirichlet variationnels non linéaires: Partie 1 des comptes rendus du cours d'été OTAN "Variational methods in nonlinear problems". Montréal, Québec, Canada: Presses de l'Université de Montréal, 1987.

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Isac, George. Complementarity problems. Berlin: Springer-Verlag, 1992.

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Book chapters on the topic "Variational problem"

1

Almgren, Frederick. "Variational problems involving varifolds." In Plateau’s Problem, 55–72. Providence, Rhode Island: American Mathematical Society, 2001. http://dx.doi.org/10.1090/stml/013/04.

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Esteban, Maria J. "A New Setting For Skyrme’s Problem." In Variational Methods, 77–93. Boston, MA: Birkhäuser Boston, 1990. http://dx.doi.org/10.1007/978-1-4757-1080-9_6.

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Flucher, Martin. "Bernoulli’s Free-boundary Problem." In Variational Problems with Concentration, 117–29. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8687-1_14.

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Meyer, Kenneth R., and Daniel C. Offin. "Variational Techniques." In Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, 345–72. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-53691-0_13.

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Meyer, Kenneth, Glen Hall, and Dan Offin. "Variational Techniques." In Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, 301–27. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-09724-4_12.

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Bahri, Abbas. "Setup of the Variational Problem." In Flow Lines and Algebraic Invariants in Contact Form Geometry, 19–35. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0021-5_3.

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Nanda, Sudarsan. "Variational Inequality and Complementarity Problem." In Springer Optimization and Its Applications, 63–78. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-9640-4_4.

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Balaj, Mircea, and Donal O’Regan. "A Generalized Quasi-Equilibrium Problem." In Nonlinear Analysis and Variational Problems, 201–11. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-1-4419-0158-3_15.

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Dontchev, Asen L. "The Constrained Linear-Quadratic Optimal Control Problem." In Lectures on Variational Analysis, 157–66. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79911-3_16.

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Luckhaus, Stephan. "The Stefan Problem with Surface Tension." In Variational and Free Boundary Problems, 153–57. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4613-8357-4_10.

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Conference papers on the topic "Variational problem"

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Carpio, A., M. L. Rapún, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Variational Methods for Inverse Conductivity Problem." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637891.

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Wang, Fengjiao, and Yali Zhao. "Split General Mixed Variational Inequality Problem." In 2nd International Conference on Electronics, Network and Computer Engineering (ICENCE 2016). Paris, France: Atlantis Press, 2016. http://dx.doi.org/10.2991/icence-16.2016.72.

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CARILLO, S., M. CHIPOT, and G. VERGARA CAFFARELLI. "A VARIATIONAL PROBLEM WITH NON-LOCAL CONSTRAINTS." In Proceedings of the 12th Conference on WASCOM 2003. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702937_0015.

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Bloch, Anthony, Margarida Camarinha, and Leonardo Colombo. "Variational obstacle avoidance problem on riemannian manifolds." In 2017 IEEE 56th Annual Conference on Decision and Control (CDC). IEEE, 2017. http://dx.doi.org/10.1109/cdc.2017.8263657.

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Raju, Vidya, and P. S. Krishnaprasad. "A variational problem on the probability simplex." In 2018 IEEE Conference on Decision and Control (CDC). IEEE, 2018. http://dx.doi.org/10.1109/cdc.2018.8619147.

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Bujorianu, Manuela L. "Variational inequalities for the stochastic reachability problem." In 2010 49th IEEE Conference on Decision and Control (CDC). IEEE, 2010. http://dx.doi.org/10.1109/cdc.2010.5718059.

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Cisło, J., J. T. Łopuszański, and P. C. Stichel. "On the inverse variational problem in classical mechanics." In Particles, fields and gravitation. AIP, 1998. http://dx.doi.org/10.1063/1.57126.

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ZHANG, JIAN. "CROSS-CONSTRAINED VARIATIONAL PROBLEM AND NONLINEAR SCHRÖDINGER EQUATION." In Proceedings of SMALEFEST 2000. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812778031_0019.

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"Split Generalized Variational Inequality and Mixed Equilibrium Problem." In International Conference Education and Management. Scholar Publishing Group, 2021. http://dx.doi.org/10.38007/proceedings.0001868.

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Han, Dongxue, and Yali Zhao. "Split general strong nonlinear quasi-variational inequality problem." In 2nd International Conference on Electronics, Network and Computer Engineering (ICENCE 2016). Paris, France: Atlantis Press, 2016. http://dx.doi.org/10.2991/icence-16.2016.57.

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Reports on the topic "Variational problem"

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Srinivasan, R. A variational principle for the Ackerberg-O'Malley resonance problem. Office of Scientific and Technical Information (OSTI), August 1987. http://dx.doi.org/10.2172/5639216.

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Yao, Jen-Chih. A basic theorem of complementarity for the generalized variational-like inequality problem. Office of Scientific and Technical Information (OSTI), November 1989. http://dx.doi.org/10.2172/5453251.

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Garcia, Pedro L. Cartan Forms and Second Variation for Constrained Variational Problems. GIQ, 2012. http://dx.doi.org/10.7546/giq-7-2006-140-153.

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Yao, Jen-Chih. Generalized quasi-variational inequality and implicit complementarity problems. Office of Scientific and Technical Information (OSTI), October 1989. http://dx.doi.org/10.2172/5395660.

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Tannenbaum, Allen. Statistical and Variational Methods for Problems in Visual Control. Fort Belvoir, VA: Defense Technical Information Center, March 2009. http://dx.doi.org/10.21236/ada531631.

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Petra, Noei, and Georg Stadler. Model Variational Inverse Problems Governed by Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, March 2011. http://dx.doi.org/10.21236/ada555315.

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Banks, H. T. On a Variational Approach to Some Parameter Estimation Problems. Fort Belvoir, VA: Defense Technical Information Center, May 1985. http://dx.doi.org/10.21236/ada161114.

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Hou, Elizabeth Mary, and Earl Christopher Lawrence. Variational Methods for Posterior Estimation of Non-linear Inverse Problems. Office of Scientific and Technical Information (OSTI), September 2018. http://dx.doi.org/10.2172/1475317.

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Moreno, Giovanni. A $\C$--Spectral Sequence Associated with Free Boundary Variational Problems. GIQ, 2012. http://dx.doi.org/10.7546/giq-11-2010-146-156.

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Yao, Jen-Chih. On mean value iterations with application to variational inequality problems. Office of Scientific and Technical Information (OSTI), December 1989. http://dx.doi.org/10.2172/5173143.

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