Source code location: https://github.com/convexbrain/Totsu/tree/master/solver/

Introduction

This C++ package provides a basic primal-dual interior-point method solver: PrimalDualIPM.

A common target problem is continuous scalar convex optimization such as LS, LP, QP, GP, QCQP and (approximately equivalent) SOCP. More specifically, \[ \begin{array}{ll} {\rm minimize} & f_{\rm obj}(x) \\ {\rm subject \ to} & f_i(x) \le 0 \quad (i = 0, \ldots, m - 1) \\ & A x = b, \end{array} \] where

variables \( x \in {\bf R}^n \)
\( f_{\rm obj}: {\bf R}^n \rightarrow {\bf R} \), convex and twice differentiable
\( f_i: {\bf R}^n \rightarrow {\bf R} \), convex and twice differentiable
\( A \in {\bf R}^{p \times n} \), \( b \in {\bf R}^p \).

Algorithm and design concepts

The overall algorithm is based on the reference: S. Boyd and L. Vandenberghe, "Convex Optimization", http://stanford.edu/~boyd/cvxbook/.

Current version utilizes Eigen http://eigen.tuxfamily.org/ for matrix and vector operations. Other external library is not required.

PrimalDualIPM is written as an abstracted class, which virtualizes objective and constraint functions (and also those derivatives). Therefore solving a specific problem requires a derived class that implements those virtual functions. One can use a pre-defined derived class such as QCQP, as well as construct a user-defined tailored version for the reason of functionality and efficiency.

Author

https://twitter.com/convexbrain Any feedback is welcome :-)