EURO 2025 Leeds
Abstract Submission

1453. Integrating Global and Robust Optimisation for Non-Convex Quadratic Programs

Invited abstract in session TB-31: Robust and Distributionally Robust Optimization - Theory and Applications, stream Stochastic and Robust optimization.

Tuesday, 10:30-12:00
Room: Maurice Keyworth 1.06

Authors (first author is the speaker)

1. Asimina Marousi
Chemical Engineering, University College London
2. Vassilis Charitopoulos
Chemical Engineering, UCL

Abstract

State-of-the-art robust optimisation algorithms for non-convex problems typically rely on global solvers to obtain robust optimal solutions. The prevailing approach involves deriving the dual reformulation utilising a global solver, either directly or adaptively. However, the dual reformulation can increase the problem complexity, and in the case of challenging non-convex problems may only yield a robust feasible solution. An alternative approach is based on an iterative robust cutting plane algorithm. In this case, significant computational time can be spent searching for a global solution that will be deemed robust infeasible. In this work, we introduce a novel algorithm that conducts a concurrent global optimality and robustness search for continuous non-convex problems. The proposed approach integrates spatial branch-and-bound with robust cutting plane algorithms. The key idea is that, while exploring the branch-and-bound tree, we assess the robustness of nodes entailing the best-found solutions. We illustrate the performance and benefits of our proposed approach through benchmark QCQP problems utilising McCormick envelopes to obtain convex lower bounds. The performance of the RsBB algorithm is compared to state-of-the-art methods that rely on global solvers. The findings of our work highlight the efficiency of the RsBB algorithm in terms of computational time and optimality convergence and give insights to the advantages of combining robustness and optimality search.

Keywords

Status: accepted

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