An interior point solver for smooth convex optimization with an application to environmental-energy-economic models

Olivier Epelly, Jacek Gondzio and Jean-Philippe Vial

Solving large-scale nonlinear economic models proves to be difficult or even out of reach for state-of-the-art solvers. We propose an algorithm which takes advantage of their possible special structure: a large dynamic linear block on one side, a small nonlinear convex block on the other one. NLPHOPDM is an implementation of an infeasible primal-dual IPM built upon HOPDM, a code for LP and convex QP. It combines ideas of a globally convergent algorithm for smooth convex NLP and the extension of the multiple centrality correctors technique to feasibility correctors. It is designed for being hooked to modeling languages such as AMPL, CUTE and GAMS. We present in this paper preliminary results relative to our research code and to commercial solvers for large-scale nonlinear convex economic problems. Our IPM approach achieves a significant computational speed-up. This is performed via the use of a library which computes exact second derivatives.

Logilab Technical Report 2000.08, Department of Management Studies, University of Geneva, Switzerland.