Algorithmics

• Interpolation and regression of models made of a sum of squares of polynomials. INRIA Research Report (2010, to appear).
• How the augmented Lagrangian algorithm can deal with an infeasible convex quadratic optimization problem, with A. Chiche. INRIA Research Report (2010, to appear).
• Optimisation Différentiable, Techniques de l'Ingénieur, document AF-1-252 (2008). [pdf]
• Global linear convergence of an augmented Lagrangian algorithm for solving convex quadratic optimization problems, with F. Delbos. Journal of Convex Analysis, 12 (2005) 45-69. 10 citations, according to Google Scholar (5-3-2010). [pdf]
• Examples of ill-behaved central paths in convex optimization, with C.C. Gonzaga and E. Karas. Mathematical Programming, 103 (2005) 63-94. [pdf]
• A truncated SQP algorithm for solving nonconvex equality constrained optimization problems, with L. Chauvier and A. Fuduli. Proceedings of the conference ``High Performance Algorithms and Software for Nonlinear Optimization", Erice, Italy, G. Di Pillo and A. Murli (eds), Kluwer Academic Publishers B.V., 2003, 146-173. [ps.gz]
• A BFGS-IP algorithm for solving strongly convex optimization problems with feasibility enforced by an exact penalty approach, with P. Armand and S. Jan, Mathematical Programming, 92 (2002) 393-424.
• A feasible BFGS interior point algorithm for solving strongly convex minimization problems, with P. Armand and S. Jan-Jégou. SIAM Journal on Optimization, 11 (2000) 199-222. 7 citations, according to MathSciNet (14-01-2009); 26 citations, according to Google Scholar (5-3-2010). [pdf]
• A trust region method based on interior point techniques for nonlinear programming, with R.H. Byrd and J. Nocedal. Mathematical Programming, 89 (2000) 149-185. 57 citations, according to MathSciNet (14-01-2009); 214 citations, according to Google Scholar (5-3-2010).
• A piecewise line-search technique for maintaining the positive definiteness of the matrices in the SQP method, with P. Armand. Computational Optimization and Applications, 16 (2000) 121-158. [pdf]
• Piecewise line-search techniques for constrained minimization by quasi-Newton algorithms. Advances in Nonlinear Programming, 1998, pg 73-103. Proceedings of the International Conference on Nonlinear Programming, Beijing, Y.-X. Yuan (ed), Kluwer.
• On the realization of the Wolfe conditions in reduced quasi-Newton methods for equality constrained optimization. SIAM Journal on Optimization, 7 (1997) 780-813. [pdf]
• A family of variable metric proximal methods, with F. Bonnans, Cl. Lemaréchal, and Cl. Sagastizábal. Mathematical Programming, 68 (1995) 15-47. 16 citations, according to MathSciNet (14-01-2009); 62 citations, according to Google Scholar (5-3-2010).
• Superlinear convergence of a reduced BFGS method with piecewise line-search and update criterion, INRIA Research Report, RR-2140 (December 1993).
• Global convergence properties of conjugate gradient methods for optimization, with J. Nocedal. SIAM Journal on Optimization, 2 (1992) 21-42. 57 citations, according to MathSciNet (14-01-2009). 341 citations, according to Google Scholar (5-3-2010). [pdf]
• Maintaining the positive definiteness of the matrices in reduced secant methods for equality constrained optimization. Mathematical Programming, 50 (1991) 1-28. 25 citations, according to Google Scholar (5-3-2010). [pdf]
• Some numerical experiments with variable-storage quasi-Newton algorithms, with C. Lemaréchal. Mathematical Programming, 45 (1989) 407-435. 33 citations, according to MathSciNet (14-01-2009); 448 citations, according to Google Scholar (5-3-2010). [pdf]
• On the local and global convergence of a reduced quasi-Newton method. Optimization, 20 (1989) 421-450. 15 citations, according to Google Scholar (5-3-2010).
• A step-size selection procedure for equality constrained optimization. Analysis and optimization of systems (Antibes, 1988), 309-320, Lecture Notes in Control and Inform. Sci., 111, Springer, Berlin, 1988.
• Mise à jour de la métrique dans les méthodes de quasi-Newton réduites en optimisation avec contraintes d'égalité. Modélisation Mathématique et Analyse Numérique, 22 (1988) 251-288. 9 citations, according to Google Scholar (5-3-2010).

Applications

• Constrained optimization in seismic reflection tomography: a Gauss-Newton augmented Lagrangian approach, with F. Delbos, R. Glowinski, and D. Sinoquet. Geophysical Journal International 164 (2006) 670-684. [pdf]
• Optimal control of a deep-towed vehicle by optimization techniques (1998), with L. Chauvier, G. Damy, and N. Pichon. Proceedings of the IEEE/OES Conference "Oceans'98", Nice, September 1998, pg 1634-1639. [pdf]

Software

• M1CG1 - A solver of symmetric linear systems by conjugate gradient iterations, using a BFGS or an l-BFGS preconditioner - Version 1.2. October 2011. [pdf]
• SQPpro - A solver of nonlinear optimization problems, using an SQP approach - Version 0.5. May, 2009. INRIA Technical Report, RT-378 (December 2009). [pdf]
• QPAL - A solver of convex quadratic optimization problems, using an augmented Lagrangian approach - Version 0.6.1. May 2009. INRIA Technical Report, RT-377 (December 2009). [pdf]
• The module M1QN3 - Version 3.3, with C. Lemaréchal. October 2009. [pdf]
• SQPlab - A Matlab software for solving nonlinear optimization problems and optimal control problems - Version 0.4.4. February 2009. [pdf]
• LIBOPT - An environment for testing solvers on heterogeneous collections of problems - The manual, version 2.1, with X. Jonsson. INRIA Technical Report, RT-331 revised (January, 2009). [pdf]
• LIBOPT - An environment for testing solvers on heterogeneous collections of problems, with X. Jonsson. Submitted to ACM Transactions on Mathematical Software, January, 2009. [pdf]
• Organization of the Modulopt collection of optimization problems in the Libopt environment - Version 2.1. INRIA Technical Report, RT-329 revised (January, 2009). [pdf]