Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms

By Jiming Peng; Cornelis Roos et al. | Go to book overview

Index
Adler, 4, 16, 69
affine scaling direction, 10
AHO direction
for SDO, 112
for SOCO, 145
Alizadeh, 100, 111
barrier degree, 29
barrier parameter, 13
barrier property, 13
basic solution, 10
bilinear operator, 130
Cauchy–Schwarz inequality, 51, 132, 141
central path, v, 28, 172
for CP, 69, 71, 72, 81
for LO, 52
for LO, 4, 8, 10, 14, 21
for SDO, 102, 103, 111, 117, 123
for SOCO, 128, 129, 142, 151
combinatorial optimization, 100
computer science, 68
cone of positive definite matrices, 29, 103, 131
cone of positive definite matrices, 115
control theory, 100
convexity theory, 32
corrector direction, 10
Dantzig, 1, 2
derivatives of functions associated with second-order cone, 139
derivatives of matrix-valued function, 108
determinant
associated with second-order cone, 131
of a matrix, 136
Dikin, 3
divided difference of a function, 108
dual HKM direction
for SDO, 112
for SOCO, 145
duality gap
for LO, 10, 11, 21
for SDO, 112
for SOCO, 150
duality theory
of LO, 6
of SDO, 101
of SOCO, 128
economic equilibrium, 68
eigenvalues
associated with second-order cone, 131
of a matrix, 104
ellipsoid method, 3
embedding model for CP, 162
Euclidean Jordan algebra
for second-order cone, 129, 130
Fukushima, 132
function
associated with the second-order cone, 129
game theory, 68
global minimizer, 68
Goldman, 6, 160

-183-

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