Algorithm 1053: SOLNP+: A Derivative-Free Solver for Constrained Nonlinear Optimization

SOLNP \(+\) is a derivative-free solver for constrained nonlinear optimization. It starts from SOLve Nonlinear Programming (SOLNP) proposed in 1989 by Ye. The main ideas are to use finite difference to approximate the gradient of the objective function and constraints, and use augmented Lagrangian method and sequential quadratic programming to deal with nonlinear constraints. We incorporate the techniques of implicit filtering, a new restart mechanism, and a modern quadratic programming solver into this new version with an ANSI C implementation. The algorithm exhibits a great advantage in running time and robustness under noise compared with the old version implemented in MATLAB. The numerical experiments show that SOLNP \(+\) is comparable with two widely used solvers, COBYLA and NOMAD. SOLNP \(+\) is available at https://github.com/COPT-Public/SOLNP_plus .