## Optimization: proceedings of the Fifth French-German Conference, held in Castel-Novel (Varetz), France, Oct. 3-8, 1988The 2-yearly French-German Conferences on Optimization review the state-of-the-art and the trends in the field. The proceedings of the Fifth Conference include papers on projective methods in linear programming (special session at the conference), nonsmooth optimization, two-level optimization, multiobjective optimization, partial inverse method, variational convergence, Newton type algorithms and flows and on practical applications of optimization. A. Ioffe and J.-Ph. Vial have contributed survey papers on, respectively second order optimality conditions and projective methods in linear programming. |

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### Contents

A smoothing technique for nondifferentiable optimization problems | 1 |

Numerical study of projective methods for linear programming | 25 |

Applications and numerical convergence of the partial inverse method | 39 |

Copyright | |

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admissible sequence affine Analysis analytic center applications approximation assume assumption compact compute concave function cone consider constraints convex function convex programming convex set CPCC(XxY defined definition denote dual Edited equations equivalent exists feasibility problem feasible point fi(x finite given graph Hence hk-i implies inequality interior interior point methods Karmarkar's Karmarkar's algorithm Lagrange multiplier Lemma linear programming linesearch Lipschitz Lipschitz continuous lower bound Math matrix minimax Newton flows Newton step Newton's method nonlinear nonlinear programming norm null space number of iterations obtain optimal solution optimization problems parameter Partial Inverse polynomial polytope primal Proceedings programming problem projective algorithm projective methods Proof PROPOSITION prove proximal quadratic resp Rockafellar saddle point satisfies search direction second order Section solving space sufficient condition Theorem Theory Topology update variables vector vertex vertices x(Xk zero