2. ESTADO DEL ARTE
2.4. Software de Comunicación Aumentativa y Alternativa con ARASAAC
T : H → G The single-valued operator T mapping from H to G . . . p. 99 Fix T The set of fixed points of a single-valued operator T . . . p. 99 ker L The kernel of a linear operator L . . . p. 66 ||L|| The norm of a linear operator L . . . p. 66 L∗ The adjoint of a linear operator L . . . p. 66 AT The transpose of a matrix A . . . p. 66 A ⊗ B The Kronecker product of two matrices A and B . . . p. 105105 Id The identity operator . . . p. 1010
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K-nearest neighbors,121121
β-inverse strongly monotone operator, 1010 ε-accuracy, 1919 adjoint, 66 affine hull, 66 almost surely, 1111 arg min, 55 averaging operator, 108108 biconjugate, 77 blur operator, 108108
bounded linear operator, 66 capital requirement, 1212 Cauchy–Schwarz inequality, 55 classical Heron problem, 113113 classification, 110110 closed ball, 55 set, 66 unit ball, 55 cluster center, 121121 clustering, 121121 cocoercive operator, 1010 concave function, 66
strictly concave function, 66 concave utility function, 1212 Conditional Value-at-Risk, 119119 cone, 66
conjugate function, 77
continuous linear operator, 66 convex function, 66
strictly convex function, 66 strongly convex function, 66 convex set, 66
convex utility function, 1212 decision function, 111111 difference operator
horizontal, 105105 vertical, 105105
discrete first-order derivative, 105105 discrete second-order derivative, 105105 distance function, 113113
domain
of a function, 66 of an operator, 1010 dual
optimal objective value, 55 problem, 55
dual unit ball, 102102
entropic risk measure, 119119 epigraph, 66 essential infimum, 1111 essential supremum, 1111 Euclidean space, 55 expectation value, 1111 expected returns, 116116
fast gradient method, 1919, 2121 Fenchel–Moreau Theorem, 77 Fermat’s rule, 88
firmly nonexpansive operator, 99, 1010 fixed point, 99
fixed point set, 99
forward difference matrix, 105105 future net worth, 1212
Gaussian noise, 106106
generalized Heron problem, 113113 Gram matrix, 111111
graph of a set-valued operator, 1010 Haar wavelet transform, 108108 Hilbert
direct sum, 55 space, 55 hinge loss, 111111
identity operator, 1010
image deblurring problem, 108108 image denoising problem, 101101, 104104 implementation errors, 8484
increasing function, 66 indicator function, 99 infimal convolution, 88
exact infimal convolution, 88 infimum, 55
inner product, 55, 1212, 111111 interior, 66
inverse of a set-valued operator, 1010 ISNR, 106106
kernel function, 111111
kernel of a linear operator, 66 Kronecker product, 105105 learning method, 111111 linear operator, 66 Lipschitz continuous, 99
Lipschitz continuous operator, 99 lower semicontinuity at a point, 77 of a function, 77 machine precision, 114114 matrix, 66 maximum, 55 minimum, 55 Minkowski sum, 55 monotone operator, 1010 maximally monotone, 1010 strongly monotone, 1010 uniformly monotone, 1010 Moreau envelope, 88, 1616, 3434
Moreau’s decomposition formula, 99, 1010 natural numbers, 55
Neumann boundary condition, 102102 nonexpansive operator, 1010
norm, 55, 1212, 111111
norm of a linear operator, 66 normal cone, 66
normalization condition, 1212 optimal solution, 55, 1919
Optimized Certainty Equivalent, 1212 orthogonal complement, 66
parallel sum, 1111
portfolio optimization problem, 115115 primal
optimal objective value, 55 problem, 55
primal-dual gap function, 5151 primal-dual solution, 4848, 8484 PRISMA algorithm, 3333 probability measure, 1111 probability space, 1111 projection operator, 99 proper function, 66 proximal point, 99
proximal point mapping, 99 random variable, 1111
range of a set-valued operator, 1010 rate of convergence, 3333, 3636
real numbers, 55
extended real line, 55 positive real numbers, 55
strictly positive real numbers, 55 recession function, 117117
reflected resolvent, 1010
reflexive boundary condition, 102102
regularization parameter, 101101, 106106, 108108, 111
111
relative interior, 66
representer theorem, 111111
Reproducing Kernel Hilbert Space, 111111 resolvent, 1010
right position, 114114 risk function, 1212
cash-invariant risk function, 1212 coherent risk measure, 1212 convex risk function, 1212 convex risk measure, 1212 monotone risk function, 1212