Optimization meets Machine Learning

This repository provides the code and all experiments used in the following paper:

“Optimization meets machine learning: an exact algorithm for semi-supervised support vector machines”
Veronica Piccialli, Jan Schwiddessen, Antonio M. Sudoso
Journal: Mathematical Programming (Series B), 2024 - DOI: 10.1007/s10107-024-02175-z

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An exact solver for L2-norm S3VMs

This repository contains reference code and scripts to solve semi-supervised SVMs (S3VMs) exactly using a branch-and-cut framework and semidefinite programming (SDP) relaxations. It also includes utilities to prepare datasets and to reproduce the computational experiments reported in the paper.

Highlights

• Strong SDP-based lower bounds using RLT cuts and optimality-based bound tightening
• Local search to build tight feasible (upper-bound) solutions from the solution of the SDP relaxation
• Reproducible experiment pipeline

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Usage

1. Prepare inputs

   • instances.txt (one instance per line)
   • parameters.txt

2. Run

mkdir -p output
julia -t auto

In the Julia REPL:

include("sdp_s3vm.jl")
run_tests("instances.txt", "parameters.txt")

All results are written to output/.