[mlpack-git] [mlpack] Implementation of primal-dual interior point SDP solver (#391)

[Stephen Tu]

The implementation is based on the XZ+ZX method presented here: https://www.cs.nyu.edu/overton/papers/pdffiles/pdsdp.pdf
You can view, comment on, or merge this pull request online at:

  https://github.com/mlpack/mlpack/pull/391

-- Commit Summary --

  * WIP: a compiling, but non-functioning primal-dual IP SDP solver
  * WIP: a compiling test case
  * WIP: hammer out a few bugs, still doesn't work
  * WIP: fix a few more bugs
  * add a check for dual feasibility
  * WIP: commit missing data file
  * restructure the primal-dual tests a bit
  * error checking of initial matrices
  * lovasz theta SDP test
  * Add log chebyshev approx testcase
  * add a comment on why the MVU test fails
  * comment out MVU test case
  * add correlation coeff sdp test from wiki
  * minor cleanup of comments
  * Add some comments/TODOs to the primal-dual implementation
  * implement the mehrotra's predictor-corrector rule
  * refactor KKT solver
  * more refactoring
  * sparse svec
  * primal dual method now takes adv of sparse constraints
  * use glibc constants
  * make the SDP objective matrix type a template parameter
  * iteration check is now iteration != maxIterations
  * Port LR-SDP to use the new SDP problem object
  * fix up PrimalDualSolver::Optimize() return value
  * Merge remote-tracking branch 'mlpack/master' into ip

-- File Changes --

    M src/mlpack/core/math/CMakeLists.txt (1)
    M src/mlpack/core/math/lin_alg.cpp (89)
    M src/mlpack/core/math/lin_alg.hpp (46)
    A src/mlpack/core/math/lin_alg_impl.hpp (23)
    M src/mlpack/core/optimizers/CMakeLists.txt (2)
    D src/mlpack/core/optimizers/lrsdp/CMakeLists.txt (13)
    A src/mlpack/core/optimizers/sdp/CMakeLists.txt (17)
    R src/mlpack/core/optimizers/sdp/lrsdp.hpp (34)
    R src/mlpack/core/optimizers/sdp/lrsdp_function.hpp (118)
    R src/mlpack/core/optimizers/sdp/lrsdp_function_impl.hpp (159)
    R src/mlpack/core/optimizers/sdp/lrsdp_impl.hpp (26)
    A src/mlpack/core/optimizers/sdp/primal_dual.hpp (133)
    A src/mlpack/core/optimizers/sdp/primal_dual_impl.hpp (386)
    A src/mlpack/core/optimizers/sdp/sdp.hpp (116)
    A src/mlpack/core/optimizers/sdp/sdp_impl.hpp (71)
    M src/mlpack/methods/matrix_completion/matrix_completion.cpp (2)
    M src/mlpack/methods/matrix_completion/matrix_completion.hpp (9)
    M src/mlpack/methods/mvu/mvu.cpp (4)
    M src/mlpack/tests/CMakeLists.txt (1)
    A src/mlpack/tests/data/r10.txt (10)
    M src/mlpack/tests/lin_alg_test.cpp (99)
    M src/mlpack/tests/lrsdp_test.cpp (24)
    A src/mlpack/tests/sdp_primal_dual_test.cpp (635)
    M src/mlpack/tests/to_string_test.cpp (4)

-- Patch Links --

https://github.com/mlpack/mlpack/pull/391.patch
https://github.com/mlpack/mlpack/pull/391.diff

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https://github.com/mlpack/mlpack/pull/391
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