André L. Tits

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reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from North-Holland. Abstract. Extension of quasi-Newton techniques from unconstrained to constrained optimization via(More)
A sequential quadratic programming (SQP) algorithm generating feasible iterates is described and analyzed. What distinguishes this algorithm from previous feasible SQP algorithms proposed by various authors is a reduction in the amount of computation required to generate a new iterate while the proposed scheme still enjoys the same global and fast local(More)
A common strategy for achieving global convergence in the solution of semi-innnite programming (SIP) problems, and in particular of continuous minimax problems, is to (approximately) solve a sequence of discretized problems, with a progressively ner discretization meshes. Finely discretized minimax and SIP problems, as well as other problems with many more(More)
We present a numerical algorithm to implement entropy-based (MN ) moment models in the context of a simple, linear kinetic equation for particles moving through a material slab. The closure for these models—as is the case for all entropy-based models—is derived through the solution of constrained, convex optimization problem. The algorithm has two(More)
A scheme|inspired from an old idea due to Mayne and Polak (Math. Prog., vol. 11, 1976, pp. 67{80)|is proposed for extending to general smooth constrained optimization problems a previously proposed feasible interior-point method for inequality constrained problems. It is shown that the primal-dual interior point framework allows for a signi cantly more e(More)
Two interior-point algorithms are proposed and analyzed, for the (local) solution of (possibly) indefinite quadratic programming problems. They are of the Newton-KKT variety in that (much like in the case of primal-dual algorithms for linear programming) search directions for the “primal” variables and the Karush-Kuhn-Tucker (KKT) multiplier estimates are(More)
∗The work of the first and third authors was supported in part by the National Science Foundation under Grants DMI-9813057 and DMI-0422931, and by the US Department of Energy under Grant DEFG0204ER25655. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the(More)
We propose an adaptive, constraint-reduced, primal-dual interior-point algorithm for convex quadratic programming with many more inequality constraints than variables. We reduce the computational effort by assembling, instead of the exact normal-equation matrix, an approximate matrix from a well chosen index set which includes indices of constraints that(More)