Interior point methods for SOS optimization. #93

bentonatura · 2020-07-02T13:00:12Z

Google Summer of Code 2020

Added features, features for future improvements and weekly progress are listed in include/sos/README.md

bentonatura · 2020-08-31T16:43:53Z

Final Status Google Summer of Code:

Implemented

The generic implementation of the algorithm in [1] with barrier methods for the following cones:
- Non-negative orthant
- SDP cone
- Dual of SOS cone with following bases:
  - monomial
  - interpolant
Generation of Lagrange polynomials for Chebyshev points of the second kind
Tool that approximates the polynomial lower envelope of any (stable to degree approx. 100) set of univariate polynomials
on the interval [-1,1].
Visualisation via Matplotlib plot.
Support for several floating-point precision data types for the IPM
(Primitive Floating Point and boost:multiprecision floats)
Added multivariate support
Added multithreading.
Added LAPACK and BLAS support
Added MKL Support (system-dependent configuration necessary)
Dynamically switch between float -> double -> long double -> multiprecision, when Matrices become ill-conditioned.
Note that this feature currenlty only works for the InterpolantDualSOSBarrier, SumBarrier and ProductBarrier.
Dynamic step-length for predictor step and size of large neighborhood.
Input and configuration files in JSON format

vissarion

Thanks Bento for this PR! I am in general OK with merging but I have a few comments as a minimum effort to conform with existing code base.

external/ChebTools/ChebTools.cpp

external/Padua/padua.cpp

vissarion · 2020-10-05T14:12:42Z

include/sos/barriers/LHSCB.h

+        return lhscb;
+    }
+
+    virtual ~LHSCB() {};


please eliminate the use of virtual functions

It is very natural to use virtual function. The Skajaa-Ye algorithm needs a Logarithmically-Homogeneous-Self-Concordant-Barrier (LHSCB) as input, which has to implement several functions. This could be the Interpolant Barrier for the dual SOS cone that we mostly use or any other barrier for the SOS cone or other conoes like the non-negative orthant or the PSD cone.
Can you please elaborate why we should implement this differently, considering that it is not a bottleneck in computation?

It's a matter of design, it is not good practice to mix designs in a library. If it is difficult to change and since this part is not interacting a lot with the rest of the library I am OK to leave as is. In any case my main concern is performance.

vissarion · 2020-10-05T14:14:05Z

include/sos/EnvelopeProblemSOS.h

+    void initialize_problem();
+};
+
+#include "EnvelopeProblemSOS.tpp"


why not just use hpp for file format of all your header files as is in the library right now ?

From what I've read it is better coding practice to use .tpp endings for the type of template classes that I am using. For consistency with the rest of code .cpp endings would be better, agreed.

For consistency with the library as it is so far I recommend to use hpp for header files too. In any case the parser does not care about file formats it is just a convention.

vissarion · 2020-10-05T14:19:07Z

include/sos/EnvelopeProblemSOS.tpp

@@ -0,0 +1,506 @@
+// VolEsti (volume computation and sampling library)


this is an application of the SOS solver, right? Could it be an example instead (placed for instance in examples/EnvelopeProblemSOS directory) since it has a lot of unfinished parts and TODOs ?

include/sos/barriers/LPStandardBarrier.h

vissarion · 2020-10-05T14:46:36Z

include/sos/barriers/ProductBarrier.tpp

+        product_vector.segment(seg.first, seg.second - seg.first) = vec_seg;
+    }
+    return product_vector;
+}


add newline at the end of file

vissarion · 2020-10-05T14:48:44Z

include/sos/include/matplotlib-cpp/matplotlibcpp.h

@@ -0,0 +1,2342 @@
+#pragma once


see comments about external libraries

vissarion · 2020-10-05T14:49:54Z

include/sos/non_symm_cone_tests/tests.cpp

@@ -0,0 +1,157 @@
+// VolEsti (volume computation and sampling library)


a better place for tests is in test directory

vissarion · 2020-10-05T14:51:22Z

include/sos/sos.cpp

@@ -0,0 +1,90 @@
+// VolEsti (volume computation and sampling library)


since this is a header only library maybe examples is a good place for this?

vissarion · 2020-10-06T10:38:50Z

include/sos/CMakeLists.txt

@@ -0,0 +1,52 @@
+cmake_minimum_required(VERSION 3.15)


this file will not be able to generate a Makefile in other computers than yours, please remove explicit paths

vissarion · 2020-10-06T10:39:15Z

include/sos/CMakeLists.txt

+add_executable(NonSymmetricConicOptimization ${TARGETS} utils.cpp)
+
+if (NOT BOOST_DIR)
+    find_package(Boost COMPONENTS *boost usr/local/)


what version of boost do you require ?

1.67 should be enough. Have not tracked exactly in which version the needed libraries where modified the last time.

ok please at this info to the README

elias-tsigaridas · 2020-10-07T10:03:53Z

include/sos/CMakeLists.txt

@@ -0,0 +1,52 @@
+cmake_minimum_required(VERSION 3.15)


I have some comments/suggests for the CMakeLists.txt file to be more "useable".
I had to make some changes to make it work.

Besides Boost, the directory of Eigen should be defined
because, among others, you use the unsupported directory.

There is also a problem with openMP, some variables are not defined.
I suggest that we add something like the following in the CMakeLists.txt
###find_package(OpenMP REQUIRED)
OPTION (USE_OpenMP "Use OpenMP to enamble <omp.h>" ON)
set(OPENMP_LIBRARIES "/opt/local/lib")
set(OPENMP_INCLUDES "/opt/local/include")

Find OpenMP

if(APPLE AND USE_OpenMP)
if(CMAKE_C_COMPILER_ID MATCHES "Clang")
set(OpenMP_C "${CMAKE_C_COMPILER}")
set(OpenMP_C_FLAGS "-fopenmp=libomp -Wno-unused-command-line-argument")
set(OpenMP_C_LIB_NAMES "libomp" "libgomp" "libiomp5")
set(OpenMP_libomp_LIBRARY ${OpenMP_C_LIB_NAMES})
set(OpenMP_libgomp_LIBRARY ${OpenMP_C_LIB_NAMES})
set(OpenMP_libiomp5_LIBRARY ${OpenMP_C_LIB_NAMES})
endif()
if(CMAKE_CXX_COMPILER_ID MATCHES "Clang")
set(OpenMP_CXX "${CMAKE_CXX_COMPILER}")
set(OpenMP_CXX_FLAGS "-Wno-unused-command-line-argument")
set(OpenMP_CXX_LIB_NAMES "libomp" "libgomp" "libiomp5")
set(OpenMP_libomp_LIBRARY ${OpenMP_CXX_LIB_NAMES})
set(OpenMP_libgomp_LIBRARY ${OpenMP_CXX_LIB_NAMES})
set(OpenMP_libiomp5_LIBRARY ${OpenMP_CXX_LIB_NAMES})
endif()
endif()

if(USE_OpenMP)
find_package(OpenMP REQUIRED)
endif(USE_OpenMP)

if (OPENMP_FOUND)
include_directories("${OPENMP_INCLUDES}")
link_directories("${OPENMP_LIBRARIES}")
set (CMAKE_C_FLAGS "${CMAKE_C_FLAGS} ${OpenMP_C_FLAGS}")
set (CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${OpenMP_CXX_FLAGS}")
# set (CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS} ${OpenMP_EXE_LINKER_FLAGS}")
endif(OPENMP_FOUND)
#######

Finally, we should variables to set the directories of
the intel compiler, python, and llvm
because they are not always live in the directories that you specify in the CMakeList.txt

Anyways, after these changes I managed to compile and run the code.

Added JSON parsing

* Add Boost Info

vissarion requested a review from TolisChal July 3, 2020 06:29

vissarion added the enhancement label Jul 3, 2020

bentonatura marked this pull request as draft July 11, 2020 12:34

vissarion self-requested a review July 27, 2020 10:46

bentonatura force-pushed the sos branch 2 times, most recently from ff68082 to 425f829 Compare July 29, 2020 07:35

bentonatura marked this pull request as ready for review July 29, 2020 09:50

bentonatura force-pushed the sos branch from 29593a3 to 93df5e0 Compare August 13, 2020 21:51

bentonatura force-pushed the sos branch from 93df5e0 to ba71eda Compare August 31, 2020 11:36

vissarion changed the title ~~IPM implementation of SOS optimization.~~ Interior point methods for SOS optimization. Oct 5, 2020

vissarion approved these changes Oct 5, 2020

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vissarion reviewed Oct 6, 2020

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elias-tsigaridas reviewed Oct 7, 2020

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vissarion force-pushed the develop branch from 835f601 to 1bd54f2 Compare October 26, 2020 10:48

bentonatura added 14 commits November 16, 2020 19:07

First version

710b8ac

fix picture

ca4b67f

fix in doc

c486758

updated Eigen library

2000804

Bug fixes. Add option to choose floating-point type for IPM

5575efb

Refactoring

08d5996

Added initialization scaling

0354ebe

Add data typ choice for IPM

a08d54d

Fixes

a81b6a2

Bug fixes and added infeasibility termination

a883a98

Added README

43ecf58

Fixes, updated README

894a0ea

Fix in loading boost

f292107

Fix in doc

a334c6f

bentonatura added 26 commits November 16, 2020 19:07

Refactoring

c702903

Refactor

5a2fe62

Refactor

ee69261

Add multivariate support. WIP

39101ef

Added bivariate and multivariate support

2fbb61c

Added multithreading. Added abstraction for Product Barrier

bef0699

Added MKL Support

048876c

Added JSON parsing

minor

d413355

Major change. Use templated double class for all algorithms

e106d5a

Refactoring

f76aac0

Revert to original Eigen Headers.

a59e1c3

Remove redundant Eigen Headers

1e984a2

Refactor

0bdb255

Added description

04b59ec

Refactoring. Fixed inheritance from Eigen/LLT

48a02c2

fix typo

d4e7d25

Move .md files

0e88a36

fixes

460d6ad

Remove SDP files

3bde159

Cleanup and removal of unused files

6bdc1bd

Minor. Add notes

82c4d85

partially addressed PR Comments

d7993f8

Move files

f9ff377

Further fixes according to PR review

96c3bb3

* Rename Files

2bba822

* Add Boost Info

Remove absolute paths in CMakeLists.txt

44d5659

bentonatura force-pushed the sos branch from f5bba37 to 44d5659 Compare November 16, 2020 19:08

TolisChal approved these changes Feb 19, 2021

View reviewed changes

Trigger Build

3bf3da2

vissarion merged commit 7cf216a into GeomScale:develop Feb 19, 2021

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Interior point methods for SOS optimization. #93

Interior point methods for SOS optimization. #93

bentonatura commented Jul 2, 2020 •

edited

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bentonatura commented Aug 31, 2020

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vissarion Oct 16, 2020

elias-tsigaridas Oct 7, 2020

		@@ -0,0 +1,506 @@
		// VolEsti (volume computation and sampling library)

		@@ -0,0 +1,157 @@
		// VolEsti (volume computation and sampling library)

		@@ -0,0 +1,90 @@
		// VolEsti (volume computation and sampling library)

Interior point methods for SOS optimization. #93

Interior point methods for SOS optimization. #93

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bentonatura commented Jul 2, 2020 • edited Loading

bentonatura commented Aug 31, 2020

Implemented

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Find OpenMP

bentonatura commented Jul 2, 2020 •

edited

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