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Theory and algorithms

Plea for a semidefinite optimization solver in complex numbers,
with Cédric Josz.
Submitted to Mathematical Programming Computation.

On the solution uniqueness characterization in the L1 norm and polyhedral gauge recovery.
Journal of Optimization Theory and Applications, online (2016).
[doi]

How the augmented Lagrangian algorithm can deal with an infeasible convex quadratic optimization problem,
with A. Chiche.
Journal of Convex Analysis, 23:2 (2016) 425459.

Optimisation Différentiable, Techniques de l'Ingénieur, document AF1252 (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) 4569.
[pdf]

Examples of illbehaved central paths in convex optimization,
with C.C. Gonzaga and E. Karas.
Mathematical Programming, 103 (2005) 6394.
[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) 146173.
[ps.gz]

A BFGSIP 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) 393424.

A feasible BFGS interior point algorithm for solving strongly convex
minimization problems,
with P. Armand and S. JanJégou.
SIAM Journal on Optimization, 11 (2000) 199222.
[pdf]

A trust region method based on interior point techniques for nonlinear
programming,
with R.H. Byrd and J. Nocedal.
Mathematical Programming, 89 (2000) 149185.

A piecewise linesearch technique for maintaining the positive definiteness of the matrices in the SQP method,
with P. Armand.
Computational Optimization and Applications, 16 (2000) 121158.
[doi]

Piecewise linesearch techniques for constrained minimization by
quasiNewton algorithms. Advances in Nonlinear Programming,
1998, pg 73103. Proceedings of the International Conference on
Nonlinear Programming, Beijing, Y.X. Yuan (ed), Kluwer.
[pdf]

On the realization of the Wolfe conditions in reduced quasiNewton
methods for equality constrained optimization.
SIAM Journal on Optimization, 7 (1997) 780813.
[pdf]

A family of variable metric proximal methods,
with F. Bonnans, Cl. Lemaréchal, and Cl. Sagastizábal.
Mathematical Programming, 68 (1995) 1547.

Superlinear convergence of a reduced BFGS method with piecewise
linesearch and update criterion,
INRIA Research Report, RR2140 (December 1993).

Global convergence properties of conjugate gradient methods for
optimization, with J. Nocedal.
SIAM Journal on Optimization, 2 (1992) 2142.
[pdf]

Maintaining the positive definiteness of the matrices in reduced secant methods for equality constrained optimization.
Mathematical Programming, 50 (1991) 128.
[pdf]

Numerical methods for largescale minimization
Proceedings of the 1991 ECMWF Seminar on "Numerical Methods in Atmospheric Models" (Reading, UnitedKingdom), 2 (1991) 93113.

Some numerical experiments with variablestorage quasiNewton algorithms,
with C. Lemaréchal.
Mathematical Programming, 45 (1989) 407435.
[pdf]

On the local and global convergence of a reduced quasiNewton method.
Optimization, 20 (1989) 421450.

A stepsize selection procedure for equality constrained optimization.
Analysis and optimization of systems (Antibes, 1988), 309320,
Lecture Notes in Control and Inform. Sci., 111, Springer, Berlin, 1988.

Mise à jour de la métrique dans les méthodes de quasiNewton
réduites en optimisation avec contraintes d'égalité.
Modélisation Mathématique et Analyse Numérique,
22 (1988) 251288.
Applications

Application of the momentSOS approach to global optimization of the OPF problem,
with C. Josz, J. Maeght, and P. Panciatici.
IEEE Transactions on Power Systems, 30:1 (2015) 463470.

Constrained optimization in seismic reflection tomography: a GaussNewton augmented Lagrangian approach,
with F. Delbos, R. Glowinski, D. Sinoquet.
Geophysical Journal International 164 (2006) 670684.
[doi]

Optimal control of a deeptowed 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 16341639.
[pdf]
Lecture notes
Software

SDOlab  A solver of real or complex number semidefinite optimization problem  Version 0.4.
March, 2017.
Available on Software
Heritage.

M1CG1  A solver of symmetric linear systems by conjugate gradient iterations, using a BFGS or an lBFGS preconditioner  Version 1.2.
October 2011.

SQPpro  A solver of nonlinear optimization problems, using an SQP approach  Version 0.5.
May, 2009.
INRIA Technical Report, RT378 (December 2009).
[pdf]

QPAL  A solver of convex quadratic optimization problems, using an augmented Lagrangian approach  Version 0.6.1
INRIA Technical Report, RT377 (May 2009).

The module M1QN3  Version 3.3,
with C. Lemaréchal.
October 2009.

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, RT331 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, RT329 revised (January, 2009).