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- J. Frédéric Bonnans, Alexander Shapiro
- SIAM Review
- 1998

This paper presents an overview of some recent, and significant, progress in the theory of optimization problems with perturbations. We put the emphasis on methods based on upper and lower estimates of the objective function of the perturbed problems. These methods allow one to compute expansions of the optimal value function and approximate optimal… (More)

- J. Frédéric Bonnans, Clóvis C. Gonzaga
- Math. Oper. Res.
- 1996

The literature on interior point algorithms shows impressive results related to the speed of convergence of the objective values, but very little is known about the convergence of the iterate sequences. This paper studies the horizontal linear complementarity problem, and derives general convergence properties for algorithms based on Newton iterations. This… (More)

This paper presents a second-order analysis for a simple model optimal control problem of a partial diierential equation, namely a well-posed semilinear elliptic system with constraints on the control variable only. The cost to be minimized is a standard quadratic functional. Assuming the feasible set to be polyhedric, we state necessary and suucient second… (More)

- J. Frédéric Bonnans, Housnaa Zidani
- SIAM J. Numerical Analysis
- 2003

- J. Frédéric Bonnans, Alexander Ioffe
- Math. Oper. Res.
- 1995

- J. Frédéric Bonnans, Julien Laurent-Varin
- Numerische Mathematik
- 2006

We derive order conditions for the discretization of (unconstrained) optimal control problems, when the scheme for the state equation is of Runge-Kutta type. This problem appears to be essentially the one of checking order conditions for symplectic partitioned Runge-Kutta schemes. We show that the computations using bi-coloured trees are naturally expressed… (More)

In the framework of Galichon, Henry-Labordère and Touzi [9], we consider the model-free no-arbitrage bound of variance option given the marginal distributions of the underlying asset. We first make some approximations which restrict the computation on a bounded domain. Then we propose a gradient projection algorithm together with a finite difference scheme… (More)

This paper deals with optimal control problems for systems affine in the control variable. We have nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain second order necessary optimality conditions. Secondly, we get a second order sufficient condition for the scalar control case.… (More)

- J. Frédéric Bonnans, Roberto Cominetti, Alexander Shapiro
- SIAM Journal on Optimization
- 1999

In this paper we discuss second order optimality conditions in optimization problems subject to abstract constraints. Our analysis is based on various concepts of second order tangent sets and parametric duality. We introduce a condition, called second order regularity, under which there is no gap between the corresponding second order necessary and second… (More)

- J. Frédéric Bonnans, Roberto Cominetti, Alexander Shapiro
- Math. Oper. Res.
- 1998

We present a perturbation theory for nite dimensional optimization problems subject to abstract constraints satisfying a second order regularity condition. We derive Lipschitz and HH older expansions of approximate optimal solutions, under a directional constraint qualiication hypothesis and various second order suucient conditions that take into account… (More)