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// used is determined by NonlinerConjuateGradientType.
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NONLINEAR_CONJUGATE_GRADIENT,
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// A limited memory approximation to the inverse Hessian is
171
// maintained and used to compute a quasi-Newton step.
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// For more details see
177
// BFGS, and it's limited memory approximation L-BFGS, are quasi-Newton
178
// algorithms that approximate the Hessian matrix by iteratively refining
179
// an initial estimate with rank-one updates using the gradient at each
180
// iteration. They are a generalisation of the Secant method and satisfy
181
// the Secant equation. The Secant equation has an infinium of solutions
182
// in multiple dimensions, as there are N*(N+1)/2 degrees of freedom in a
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// symmetric matrix but only N conditions are specified by the Secant
184
// equation. The requirement that the Hessian approximation be positive
185
// definite imposes another N additional constraints, but that still leaves
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// remaining degrees-of-freedom. (L)BFGS methods uniquely deteremine the
187
// approximate Hessian by imposing the additional constraints that the
188
// approximation at the next iteration must be the 'closest' to the current
189
// approximation (the nature of how this proximity is measured is actually
190
// the defining difference between a family of quasi-Newton methods including
191
// (L)BFGS & DFP). (L)BFGS is currently regarded as being the best known
192
// general quasi-Newton method.
194
// The principal difference between BFGS and L-BFGS is that whilst BFGS
195
// maintains a full, dense approximation to the (inverse) Hessian, L-BFGS
196
// maintains only a window of the last M observations of the parameters and
197
// gradients. Using this observation history, the calculation of the next
198
// search direction can be computed without requiring the construction of the
199
// full dense inverse Hessian approximation. This is particularly important
200
// for problems with a large number of parameters, where storage of an N-by-N
201
// matrix in memory would be prohibitive.
203
// For more details on BFGS see:
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// Broyden, C.G., "The Convergence of a Class of Double-rank Minimization
206
// Algorithms,"; J. Inst. Maths. Applics., Vol. 6, pp 76–90, 1970.
208
// Fletcher, R., "A New Approach to Variable Metric Algorithms,"
209
// Computer Journal, Vol. 13, pp 317–322, 1970.
211
// Goldfarb, D., "A Family of Variable Metric Updates Derived by Variational
212
// Means," Mathematics of Computing, Vol. 24, pp 23–26, 1970.
214
// Shanno, D.F., "Conditioning of Quasi-Newton Methods for Function
215
// Minimization," Mathematics of Computing, Vol. 24, pp 647–656, 1970.
217
// For more details on L-BFGS see:
175
219
// Nocedal, J. (1980). "Updating Quasi-Newton Matrices with Limited
176
220
// Storage". Mathematics of Computation 35 (151): 773–782.
312
362
// Write out the linear least squares problem to the directory
313
// pointed to by Solver::Options::lsqp_dump_directory as a protocol
314
// buffer. linear_least_squares_problems.h/cc contains routines for
315
// loading these problems. For details on the on disk format used,
316
// see matrix.proto. The files are named lm_iteration_???.lsqp.
319
// Write out the linear least squares problem to the directory
320
363
// pointed to by Solver::Options::lsqp_dump_directory as text files
321
364
// which can be read into MATLAB/Octave. The Jacobian is dumped as a
322
365
// text file containing (i,j,s) triplets, the vectors D, x and f are
352
407
SparseLinearAlgebraLibraryType* type);
409
const char* DenseLinearAlgebraLibraryTypeToString(
410
DenseLinearAlgebraLibraryType type);
411
bool StringToDenseLinearAlgebraLibraryType(
413
DenseLinearAlgebraLibraryType* type);
354
415
const char* TrustRegionStrategyTypeToString(TrustRegionStrategyType type);
355
416
bool StringToTrustRegionStrategyType(string value,
356
417
TrustRegionStrategyType* type);
371
432
const char* NonlinearConjugateGradientTypeToString(
372
433
NonlinearConjugateGradientType type);
373
434
bool StringToNonlinearConjugateGradientType(
374
string value, NonlinearConjugateGradientType* type);
436
NonlinearConjugateGradientType* type);
438
const char* LineSearchInterpolationTypeToString(
439
LineSearchInterpolationType type);
440
bool StringToLineSearchInterpolationType(
442
LineSearchInterpolationType* type);
444
const char* CovarianceAlgorithmTypeToString(
445
CovarianceAlgorithmType type);
446
bool StringToCovarianceAlgorithmType(
448
CovarianceAlgorithmType* type);
376
450
const char* LinearSolverTerminationTypeToString(
377
451
LinearSolverTerminationType type);
added
removed
extern/libmv/third_party/ceres/include/ceres/types.h
