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A Computationally Efficient Feasible Sequential Quadratic Programming Algorithm
 SIAM Journal on Optimization
, 2001
"... . 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 pr ..."
Abstract

Cited by 56 (0 self)
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. 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 convergence properties. A preliminary implementation has been tested and some promising numerical results are reported. Key words. sequential quadratic programming, SQP, feasible iterates, feasible SQP, FSQP AMS subject classifications. 49M37, 65K05, 65K10, 90C30, 90C53 PII. S1052623498344562 1.
Nonmonotone Line Search for Minimax Problems
, 1993
"... . It was recently shown that, in the solution of smooth constrained optimization problems by sequential quadratic programming (SQP), the Maratos effect can be prevented by means of a certain nonmonotone (more precisely, threestep or fourstep monotone) line search. Using a well known transformation ..."
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Cited by 23 (2 self)
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. It was recently shown that, in the solution of smooth constrained optimization problems by sequential quadratic programming (SQP), the Maratos effect can be prevented by means of a certain nonmonotone (more precisely, threestep or fourstep monotone) line search. Using a well known transformation, this scheme can be readily extended to the case of minimax problems. It turns out however that, due to the structure of these problems, one can use a simpler scheme. Such a scheme is proposed and analyzed in this paper. Numerical experiments indicate a significant advantage of the proposed line search over the (monotone) Armijo search. Key words. Minimax problems, SQP direction, Maratos effect, Superlinear convergence. 1 This research was supported in part by NSF's Engineering Research Centers Program No. NSFDCDR88 03012, by NSF grant No. DMC8815996 and by a grant from the Westinghouse Corporation. 2 To whom the correspondence should be addressed. 1. Introduction. Consider the "m...
An SQP Algorithm For Finely Discretized Continuous Minimax Problems And Other Minimax Problems With Many Objective Functions
, 1996
"... . A common strategy for achieving global convergence in the solution of semiinfinite programming (SIP) problems, and in particular of continuous minimax problems, is to (approximately) solve a sequence of discretized problems, with a progressively finer discretization meshes. Finely discretized min ..."
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Cited by 20 (2 self)
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. A common strategy for achieving global convergence in the solution of semiinfinite programming (SIP) problems, and in particular of continuous minimax problems, is to (approximately) solve a sequence of discretized problems, with a progressively finer discretization meshes. Finely discretized minimax and SIP problems, as well as other problems with many more objectives /constraints than variables, call for algorithms in which successive search directions are computed based on a small but significant subset of the objectives/constraints, with ensuing reduced computing cost per iteration and decreased risk of numerical difficulties. In this paper, an SQPtype algorithm is proposed that incorporates this idea in the particular case of minimax problems. The general case will be considered in a separate paper. The quadratic programming subproblem that yields the search direction involves only a small subset of the objective functions. This subset is updated at each iteration in such a wa...
A sequential quadratically constrained quadratic programming method for . . .
 JOURNAL OF MATHEMATICAL ANALYSIS AND
, 2010
"... ..."
Some Properties of Trust Region Algorithms for Nonsmooth Optimization
, 1983
"... This paper discusses some properties of trust region algorithms for nonsmooth optimization. The problem is expressed as the minimization of a function h(f(x)), where h(:) is convex and f is a continuously differentiable mapping from ! n to ! m . Conditions for the convergence of a class of algor ..."
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Cited by 3 (1 self)
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This paper discusses some properties of trust region algorithms for nonsmooth optimization. The problem is expressed as the minimization of a function h(f(x)), where h(:) is convex and f is a continuously differentiable mapping from ! n to ! m . Conditions for the convergence of a class of algorithms are discussed, and it is shown that the class includes minimax and L1 problems. Key words: Trust Region Algorithms, Nonsmooth Optimization, KuhnTucker Points. Technical Report: DAMTP 1983/NA4 1. Introduction Many papers have been published on trust region algorithms, for example see Mor'e(1982). Powell (1970, 1975, 1983) and Sorensen (1982), but most attention has been given to the smooth case. We investigate some properties of trust region algorithms for nonsmooth cases. The problem we went to solve is min x2! n h(f(x)); (1.1) where h(:) is a convex function defined on ! m and is bounded below; f(x) = (f 1 (x); : : : ; fm (x)) T is a map from ! n to ! m and f i (x)(i = ...
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"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: