qptools 1.0.3

Fast quadratic programming tools (with CUDA support)

qptools

Fast quadratic programming tools.

中文 | English

Platforms

• Windows: To Do
• Linux: Supports CPU and CUDA versions
• MacOS: Supports CPU version

Dependencies

• setuptools
• pybind11
• numpy
• CUDA Toolkits for CUDA supports

Installation

CPU version

Install the package without CUDA support

pip install qptools

CUDA version

export CUDA_HOME=(your cuda path)
export USE_CUDA=1
pip install qptools

Solving Quadratic Programming Problems

qp1: Basic Quadratic Programming

$$ \min_{x} \frac12 x^TPx+q^Tx \ \text{s.t. } lb \leq x \leq rb, \ Gx \leq h $$

where $P$ is a $n\times n$ positive definite matrix, $q$ is an $n$-dimensional vector, $G$ is a $g\times n$ matrix, $h$ is a $g$-dimensional vector, and $lb,rb$ are $n$-dimensional vectors defining the lower and upper bounds for variable $x$.

qp2: Quadratic Programming with Standardized Variables

$$ \min_{x} \frac12 x^TPx+q^Tx \ \text{s.t. } lb \leq \frac{x}{\text{sum}(x)} \leq rb, \ Gx \leq h $$

where $P$ is a $(n,n)$ positive definite matrix, $q$ is an $n$-dimensional vector, $G$ is a $(g,n)$ matrix, $h$ is a $g$-dimensional vector, and $lb,rb$ are $n$-dimensional vectors defining the lower and upper bounds for standardized variable $\frac{x}{\sum(x)}$.

Example

• Python (CPU): ./example/cpu.ipynb
• Python (CUDA): ./example/cuda.ipynb
• C++ (CPU): ./c/core/test/test.cpp
• C++ (CUDA): ./c/core/test/test.cu

References

1. Nesterov, Y., & Todd, M. J. (1997). Self-scaled barriers and interior-point methods for convex programming. Mathematics of Operations Research, 22(1), 1-42.

2. Nesterov, Y., & Todd, M. J. (1998). Primal-dual interior-point methods for self-scaled cones. SIAM Journal on Optimization, 8(2), 324-364.

3. Mehrotra, S. (1992). On the implementation of a primal-dual interior point method. SIAM Journal on Optimization, 2(4), 575-601.