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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)

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 drastic reduction in the amount of computation required to generate a new iterate while the proposed scheme still enjoys the same global and fast… (More)

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)

- Jin Hyuk, Jung, Dianne P O 'leary, André L Tits
- 2007

A support vector machine (SVM) determines whether a given observed pattern lies in a particular class. The decision is based on prior training of the SVM on a set of patterns with known classification, and training is achieved by solving a convex quadratic programming problem. Since there are typically a large number of training patterns, this can be… (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)

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan, sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will… (More)

Given a primal-dual pair of linear programs, it is well known that if their optimal values are viewed as lying on the extended real line, then the duality gap is zero, unless both problems are infeasible, in which case the optimal values are +∞ and −∞. In contrast, for optimization problems over nonpolyhedral convex cones, a nonzero duality gap can exist… (More)

An exact-penalty-function-based 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 any given feasible interior-point method for inequality constrained problems. It is shown that the primal-dual interior-point framework allows for a… (More)