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Pironneau, O.

Publications and source records attributed to Pironneau, O..

4 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Optimum Shape Design Using Automatic Differentiation in Reverse Mode

This paper shows how to use automatic differentiation in reverse mode as a powerful tool in optimization procedures. It is also shown that for aerodynamic applications the gradients have to be as accurate as possible. In particular, the effect of having the exact gradient of he first or second order spatial discretization schemes is presented. We show that the loss of precision in the gradient affects not only the convergence, but also the final shape. Both two and three dimensional configurations of transonic and supersonic flows have been investigated. These cases involve up to several thousand control parameters.

Hafez, M.↗
NASA NTRS1973

A dual method for optimal control problems with initial and final boundary constraints.

This paper presents two new algorithms belonging to the family of dual methods of centers. The first can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states. The second one can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states and with affine instantaneous inequality constraints on the control. Convergence is established for both algorithms. Qualitative reasoning indicates that the rate of convergence is linear.

Pironneau, O.↗
NASA NTRS1973

Rate of convergence of a class of methods of feasible directions.

This paper deals with the rate of convergence of four methods of feasible directions: the Zoutendijk procedures 1 and 2 and two modifications of these procedures due to the authors. It is shown that of these methods, the two due to the authors converge linearly under convexity assumptions, that the Zoutendijk procedure 2 converges sublinearly under these assumptions, and that the Zoutendijk procedure 1 converges linearly provided the solution of the problem is a vertex of the constraint set.

Pironneau, O.↗