Project manager at the CMA

Project duration

09/2021 – 08/2024

Research teams involved at the CMA

Data and machine learning / Mathematical optimisation

Project type

PGMO – The Gaspard Monge Programme for Optimisation, Operational Research and their Interaction with Data Science (Fondation Mathématique Jacques Hadamard)

Partners

• Prof. Michel Théra, Professor Emeritus at XLIM (UMR-CNRS 7252) – University of Limoge, Adjoint Professor at Federation University Australia, Ballarat.

• Dr. Minh N. Dao, Lecturer, Federation University, Australia

• HdR. Dr. Welington de Oliveira, teacher-researcher, Centre de Mathématiques Appliquées Mines Paris – PSL

• HdR. Dr. Ir. Wim van Ackooij, Expert researcher | EDF R&D OSIRIS département

Project description

This project focuses on theoretical and practical foundations for the design and analysis of novel scalable optimization methods. The emphasis is on solving large-scale non-convex problems resulting from energy applications. The main idea is to deliver an innovative mathematical framework along with efficient algorithms for a broad class of complex and structured problems, particularly for fractional programming. Since large-scale complex optimization problems are also encountered in machine learning, the tools developed within our research should serve largely beyond energy applications.

Publications and communications as part of the project

Articles

1. Júdice, J., Sessa, V., Fukushima, M. Solution of Fractional Quadratic Programs on the Simplex and Application to the Eigenvalue Complementarity Problem. J Optim Theory Appl (2022). https://doi.org/10.1007/s10957-022-02019-w
2. Abbasi, M. and Théra, M. Strongly regular points of mappings. Fixed Point Theory Algorithms Sci Eng (2021) 2021:14 https://doi.org/10.1186/s13663-021-00699-z
3. Van Ngai, H., Tron N. G., Van Vu, N., Théra, M. Variational Analysis of Paracvonvex Multifunctions. J Optim Theory Appl (2022).https://doi.org/10.1007/s10957-022-02021-2] 4. Wei, Z., Théra, M., Yao J-C. Characterizations of Stability of Error Bounds for Convex Inequality Constraint Systems. Open Journal of Mathematical Optimization (2022) https://doi.org/10.5802/ojmo.13
5. Dao, M. N, Saoud, H., Théra, M. Locating and Invariance Theorems of Differential Inclusions Governed by Maximally Monotone Operators, (to appear)
6. Wei, Z. Théra, M., Yao, J.C. Primal Characterizations of Error Bounds for Composite-convex Inequalities. (to appear)
7. de Oliveira, W. Computing directional stationary points for a class of nonconvex and nonsmooth optimization problems via Frank-Wolfe-like algorithms. (submitted)
8. Van Ngai, H., Tron N. G., Van Vu, N., Théra, M. Variational Analysis of Paracvonvex Multifunctions. J Optim Theory Appl (2022).https://doi.org/10.1007/s10957-022-02021-2] 9. Wei, Z., Théra, M., Yao J-C. Characterizations of Stability of Error Bounds for Convex Inequality Constraint Systems. Open Journal of Mathematical Optimization (2022) https://doi.org/10.5802/ojmo.13
10. de Oliveira, W. Computing directional stationary points for a class of nonconvex and nonsmooth optimization problems via Frank-Wolfe-like algorithms. (to appear)
11. Pham, T.N., Dao, M.N., Shah, R., Sultanova, N., Li, G. and Islam, S. A proximal subgradient algorithm with extrapolation for structured nonconvex nonsmooth problems.
(to appear)

Communications

1. Júdice, J., Sessa, V., Fukushima, M. Solution of Fractional Quadratic Programs on the Simplex and Application to the Eigenvalue Complementarity Problem. . (PGMO Days 2021)
2. Demassey, S., Sessa, V., Tavakoli, A. Optimizing over Nonlinear Networks with Duality Cuts. (PGMO Days 2021)
3. de Oliveira, W. Risk-Averse Stochastic Programming and Distributionally Robust Optimization Via Operator Splitting. (PGMO Days 2021)
4. Abassi, M., Théra, M. Characterizing the error bound properties of functions
in metrizable topological vector spaces. (PGMO Days 2021)
5. Tavakoli, A., Demassey, S., Sessa, V. Investigating the hybrid use of operations research and machine learning tools in the pump scheduling decision-making problem. SophIA Summit, Nov 2021, Sophia Antipolis, France.
6. Júdice, J., Sessa, V., Fukushima, M. On the Global Optimization of the Standard Quadratic Programming Problem (Conference Global Optimization Workshop 2022 (HUGO22))
7. Júdice, J., Sessa, V., Fukushima, M. A Two-Phase Sequential Algorithm for Global Optimization of the Standard Quadratic Programming Problem (PGMO Days 2022)
8. de Oliveira, W. , de Oliveira Souza, J. C. Progressive decoupling of linkages in a class of optimization problems with non-elicitable convexity. (PGMO Days 2022)
9. van Ackooij, W., Demassey, S., de Oliveira, W. and Syrtseva, K. Minimizing the difference of convex and weakly convex functions via bundle method. (PGMO Days 2022)
10. Théra, M. Locating and invariance theorems of differential inclusions governed by maximally monotone operators. (Optimal Transport and Uncertainty- 6-7 September 2022)