alfonso is an open-source (Octave-compatible) Matlab package for solving convex optimization problems in conic form, created by Dávid Papp and Sercan Yıldız. It enables optimization over any convex cone as long as a suitable barrier is available for either the cone or its dual. This includes many nonsymmetric cones, for example, hyperbolicity cones and their duals (such as sum-of-squares cones), semidefinite and second-order cone representable cones, power cones, and the exponential cone. It also offers performance advantages for problems whose symmetric cone programming representation requires a large number of auxiliary variables or has a special structure that can be exploited in the barrier computation.
The interfaces of the software are described in the accompanying software paper:
D. Papp and S. Yıldız. alfonso: Matlab package for nonsymmetric conic optimization. arXiv:2101.04274 https://arxiv.org/abs/2101.04274
The package also includes an implementation of the sum-of-squares optimization algorithm based on non-symmetric conic optimization and polynomial interpolants presented in:
D. Papp and S. Yıldız. Sum-of-squares optimization without semidefinite programming. SIAM Journal on Optimization 29(1), 2019, pp. 822-851. https://doi.org/10.1137/17M1160124
The code is distributed under the 2-Clause BSD License.
To cite alfonso, please mention the research article for which the code was originally developed and the software itself.
alfonso is entirely written in Matlab m-code. To install, unzip the downloaded files in any directory and add the src subdirectory to the Matlab (or Octave) path.
The polynomial optimization (sum-of-squares) examples in examples/poly_opt/ require the following additional software:
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Padua2DM(a Matlab/Octave package by M. Caliari, S. De Marchi, A. Sommariva, and M. Vianello for interpolation and cubature at the Padua points): download to any directory and add its directory to the Matlab path. -
Chebfun(an open-source package for numerical computing with functions): download and install following the installation instructions. Our code has been developed and tested with Chebfun version 5.5.0. -
partitions(a function by John D'Errico to compute all partitions of an integer): download to any directory and add its directory to the Matlab path.
src: source files for alfonso. Usealfonso.mfor the oracle interface,alfonso_simplefor the simple interface.examples: contains a number of optimization problems solved withalfonsooralfonso_simple:examples/random_lp: solves a random linear programming problem using either interface.examples/exp_design: solves an optimal design of experiments problem.examples/poly_opt: solves various polynomial optimization problems using sum-of-squares optimization.examples/portfolio: solves a mean-risk portfolio optimization problem with a factor risk model and market impact.
This package is based on a infeasible-start primal-dual interior-point algorithm that originally appeared in:
A. Skajaa and Y. Ye, A homogeneous interior-point algorithm for nonsymmetric convex conic optimization, Mathematical Programming Ser. A, 150 (2015), pp. 391-422. https://doi.org/10.1007/s10107-014-0773-1
The implementation is derived from the corrected analysis of this algorithm presented in:
D. Papp and S. Yıldız. On “A homogeneous interior-point algorithm for nonsymmetric convex conic optimization”. https://arxiv.org/abs/1712.00492
The code in residual3p.m is an implementation of the triple-precision accumulated inner product and residual computation. It was adapted from the code of Cleve Moler from a MATLAB Central blog post.