Paul Armand

Determination of the efficient set in multiobjective linear programming

This paper develops a method for finding the whole set of efficient points of a multiobjective linear problem. Two algorithms are presented; the first one describes the set of all efficient vertices and all efficient rays of the constraint polyhedron, while the second one generates the set of all efficient faces. The method has been tested on several examples for which numerical results are reported.

Finding all maximal efficient faces in multiobjective linear programming

An algorithm for finding the whole efficient set of a multiobjective linear program is proposed. From the set of efficient edges incident to a vertex, a characterization of maximal efficient faces containing the vertex is given. By means of the lexicographic selection rule of Dantzig, Orden and Wolfe, a connectedness property of the set of dual optimal bases associated to a degenerate vertex is proved. An application of this to the problem of enumerating all the efficient edges incident to a degenerate vertex is proposed. Our method is illustrated with numerical examples and comparisons with Armand—Maliverts algorithm show that this new algorithm uses less computer time.

A Feasible BFGS Interior Point Algorithm for Solving Convex Minimization Problems

We propose a BFGS primal-dual interior point method for minimizing a convex function on a convex set defined by equality and inequality constraints. The algorithm generates feasible iterates and consists in computing approximate solutions of the optimality conditions perturbed by a sequence of positive parameters

Dynamic updates of the barrier parameter in primal-dual methods for nonlinear programming

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From global to local convergence of interior methods for nonlinear optimization

converging to zero. We prove that it converges q-superlinearly for each fixed

Study of a primal-dual algorithm for equality constrained minimization

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First experimental demonstration of temporal hypertelescope operation with a laboratory prototype

. We also show that it is globally convergent to the analytic center of the primal-dual optimal set when

A globally and quadratically convergent primal–dual augmented Lagrangian algorithm for equality constrained optimization

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A local convergence property of primal-dual methods for nonlinear programming

tends to 0 and strict complementarity holds.

Spatially dispersive scheme for transmission and synthesis of femtosecond pulses through a multicore fiber

Abstract We introduce a framework in which updating rules for the barrier parameter in primal-dual interior-point methods become dynamic. The original primal-dual system is augmented to incorporate explicitly an updating function. A Newton step for the augmented system gives a primal-dual Newton step and also a step in the barrier parameter. Based on local information and a line search, the decrease of the barrier parameter is automatically adjusted. We analyze local convergence properties, report numerical experiments on a standard collection of nonlinear problems and compare our results to a state-of-the-art interior-point implementation. In many instances, the adaptive algorithm reduces the number of iterations and of function evaluations. Its design guarantees a better fit between the magnitudes of the primal-dual residual and of the barrier parameter along the iterations.