349. Global and Robust Optimisation for Non-Convex Quadratically Constrained Quadratic Programs
Invited abstract in session TC-4: Global Optimization advances, stream Global optimization.
Tuesday, 14:00-16:00Room: B100/5013
Authors (first author is the speaker)
| 1. | Asimina Marousi
|
| Chemical Engineering, University College London | |
| 2. | Vassilis Charitopoulos
|
| Chemical Engineering, UCL |
Abstract
Solving non-convex problems under uncertainty introduces additional complexity compared to their deterministic counterparts. State-of-the-art robust optimisation algorithms typically follow two approaches: utilising local solvers to obtain robust feasible solutions or leveraging global solvers to ensure robust optimality, often at a significantly higher computational cost. In this work, we propose a novel algorithm integrating global and robust optimisation methods to solve continuous non-convex quadratically constrained quadratic programming (QCQP) problems under convex uncertainty sets. The proposed Robust spatial branch-and-bound (RsBB) algorithm combines the principles of spatial branch-and-bound (sBB) with robust cutting planes. Our research hypothesis is that integrated exploration of global and robust optimality can yield computational benefits. The RsBB algorithm utilises McCormick envelopes to obtain convex lower bounds. At each node, a local solver tackles the non-convex problem. If the solution matches the best found so far, an infeasibility test assesses its robustness; otherwise, cutting planes are added to both the non-convex and convex problems. The performance of the RsBB algorithm is compared with state-of-the-art methods that rely on global solvers. The findings of our work highlight the efficiency of the RsBB algorithm and provide insights to the advantages of combining robustness and optimality search.
Keywords
- Global optimization
- Optimization under uncertainty
Status: accepted
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