COPT: A C++ Open Optimization Library

Transcription

1 COPT: A C++ Open Optimization Library {Zhouwang Yang, Ruimin Wang}@MathU School of Mathematical Science University of Science and Technology of China

2 Zhouwang Yang Ruimin Wang University of Science and Technology of China (USTC)

3 Mathematical Optimization The selection of a best element from some set of available alternatives Long history Fermat & Lagrange: calculus based formulas Newton & Gauss: iterative method

4 Mathematical Optimization Various subfields Convex programming Integer programming Fractional programming Nonlinear programming Stochastic programming Robust programming Dynamic programming Combinatorial optimization Infinite dimensional optimization

5 Mathematical Optimization Very useful in many fields Industry Bioinformatics Financial engineering Machine learning/data mining A lot of models and algorithms

6 Mathematical Optimization A lot of similarities among different problems Minimize or maximize certain energy function Specific constraint is asked to be satisfied Aframeworkcanbedesigned

7 Motivation Huge amount of algorithms A lot of repeated work (very low reusability) Existing tools Matlab optimization toolbox (commercial) Scipy (free) Various open libraries (C/C++, Python, )

8 Motivation Hard to follow and extend Matlab actually uses C as underlying code So does Python Framework differs a lot from each other in open libraries

9 Motivation To build a domestic library for optimization study A fast implementation For researchers/ followers A good opportunity to train coding skills For students

10 Target Create an optimization library (Domestic, Created in China) Integrate existing resources Flexible enough for different problems

11 Target Open source Cross platform IDE independent skills gcc, g++, gfotran MakeFile or CMakeList.txt Carefully designed interface

12 Benefit Provide an easy to code framework for doing optimization related study Enhance the communication with industry Improve coding skills of the students in the Society of Mathematical Programming

13 Why C++ Performance per $ Power: driver at all scales Size: limits on processor resources Experience: bigger experience on smaller hardware

14 Why C++

15 Why C++

16 Why C++ Efficiency Flexibility Abstraction Productivity

17 Matlab Not object oriented No unified form of code Hard for Encapsulation ( 难以封装 ) Interface Commercial

18 Python Efficiency Script Great Language Easy for learning API is provided

19 COPT C++ Open Optimization Library Created in China Proposed by the Society of Mathematical Programming Developed by MathU

20 COPT Designer: Ruimin Wang Bachelor degree in USTC in 2011 PhD candidate in USTC since 2011 Academic experience Decoupling features and noises via analysis based compressed sensing (2012) Shape modeling by drawing (2012) Point based differential computation (2013) Manifold construction via dictionary learning (2013) Sparse representation with parameterization optimization (2014) Sparsity in geometry (2014)

21 COPT C++ based open source library A lot of templates are used for flexibility An important feature of C++ Python interface is provided Great for novel user

22 COPT Brief Introduction Carefully designed basic types Array, VectorBase, MatrixBase ScalarFunction, VectorFunction Solver Other people can extend by deriving the types Some algorithms been implemented Least squares BFGS

23 A Simple Example Define the scalar type

24 A Simple Example Define the scalar type Define the Array, basic class for vector and matrix

25 A Simple Example Define the scalar type Define the Array, basic class for vector and matrix Define the Vector and Matrix

26 Operations

27 Operations Array like assignment Matlab like assignment is also allowed: like vec1(0)=1

28 Operations

29 Operations

30 Operations

31 Operations Output:

32 Operations

33 Operations Pre defined special matrix

34 Operations

35 Operations Solving linear system

36 Operations

37 COPT What have been done: A friendly designed interface Clear base class Basic operations Linear algebra Function differential (numerical) The interface of a solver

38 COPT Focus An easy to code developing framework Cross platform consideration Linux: Ubuntu Windows Max OS X Developing environment OS X Yosemite with clang MinGW on windows with g++ IDE independent

39 Dependency Classical libraries for linear operations: Blas (fortran), cblas(c), lapack(fortran) C++ template library linear algebra Eigen (maybe temporary)

40 IDE independent Integrated Development Environment( 集成开发环境 ) Visual studio Qt Creator Xcode Compiling details are ignored Link

41 IDE independent Integrated Development Environment( 集成开发环境 ) Visual studio Qt Creator Xcode Compiling details are ignored Link

42 IDE independent Still un familiar with C++ compiling Focus on code not project Light weight development

43 GitHub GitHub isa Git repository web based hosting service. It offers all of the distributed revision control and source code management. It provides a web based graphical interface and desktop.

44 A Simple Example Nonlinear optimization Steepest descent method Newton s Method Quasi Newton Method (like BFGS) A famous 2 dimensional test function Rosenbrock function f (x) x 2 x x 2 1

45 A Simple Example

46 A Simple Example

47 A Simple Example

48 A Simple Example

49 Stuff Students in MathU: Ruimin Wang, Songtao Guo, Jingyuan Hu, Baiyu Chen,

50 More Interface provided for Python Done by Songtao Guo

51 More Unified definition of function A base class is defined Automatically differential computation Many algorithms have not been implemented yet Constrained non linear optimization Large scale solvers: interior point method, alternating direction method of multipliers

52 More COPT v0.1 will be published before Jan for developers only Still a lot of remaining work Everyone is welcomed A very interesting project A good opportunity to challenge yourself

53 Join Us!