Calculus of Variations

By H. Piaggio. 1954

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Citations in the corpus

Improving Task-free Continual Learning by Distributionally Robust Memory Evolution (2022, methodology): “By calculus of variation (Miersemann, 2012), the ﬁrst variation for the KL divergence and V ( µ ) are (Ambrosio et al., 2008): Langevin Dynamics for Dynamic DRO.”
Spike-and-Slab Sparse Coding for Unsupervised Feature Discovery (2012, background): “(4) is an instance of the Euler-Lagrange equation (Gelfand, 1963), we find that the solution must take the form”
A fractional calculus of variations for multiple integrals with application to vibrating string (2010, background): “Knowing the importance and relevance of multidimensional problems of the calculus of variations in physics and engineering [43], it is at a first view surprising that a multidimensional FCV is a completely open research area.”
Liquid crystal lenses with tunable focal length (2017, background): “The minimization leads to the following Euler–Lagrange equations [249,250]:”
Derivation and physical interpretation of general boundary conditions (2006, background): “[19]) that a function u can be a minimizer of the action only if the the first variation of S, δS [u] , vanishes.”
Fractional calculus of variations for a combined Caputo derivative (2011, background): “23–537; DOI: 10.2478/s13540-011-0032-6. 1 2 A.B.MALINOWSKA,D.F.M.TORRES The calculus of variations is an old branch of optimization theory that has many applications both in physics and geometry (cf. [28, 33, 42, 43] and references therein). Apart from a few examples known since ancient times such a”
Sensitivity analysis of the climate of a chaotic system (2000, background): “Thus, z 2 appears to behave like a Weierstrass function (McShane, 1989), at least in the rangeIn practice, for the case of sensitivity to many parameters, the direct method becomes prohibit- 25∏r∏50; that is, it is apparently continuous but its local gradients are undefined.ively expensive.”
THE USE OF ADOMIAN DECOMPOSITION METHOD FOR SOLVING PROBLEMS IN CALCULUS OF VARIATIONS (2006, methodology): “The direct method of Ritz and Galerkin has been investigated for solving variational problems in [16, 17].”
Progress in the development of exchange-correlation functionals (2005, unknown): “the exchange-correlation potential is given by the rules of calculus of variations [280]”
CHOMP: Covariant Hamiltonian optimization for motion planning (2013, methodology): “Borrowing techniques from the analysis of direct methods in the calculus of variations (particularly the method of finite differences (Gelfand and Fomin, 1963)), one can show that the limit of these results as our discretization becomes increasingly fine converges to the prescribed functional…”
A phase field model of deformation twinning: Nonlinear theory and numerical simulations (2011, background): “Substantial literature [38,39] has been dedicated to assessment of existence of minimizers such as in (24).”
The variational approximation for Bayesian inference (2008, methodology): “This area of mathematics is called calculus of variations [18] and has been applied to many areas of mathematics, physical sciences and engineering, for example fluid mechanics, heat transfer, and control theory.”
Image Segmentation Using Active Contours Driven by the Bhattacharyya Gradient Flow (2007, background): “The above sequence of level-set functions can be conveniently constructed using the variational framework [32].”
Control: A perspective (2014, background): “There was a revitalization of the classical calculus of variations which has its origins in the Brachistochrone problem posed by Bernoulli in 1696 [246].”