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SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
, 2002
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 597 (24 self)
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available, and that the constraint gradients are sparse. We discuss
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 ..."
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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.
A sequential quadratic programming algorithm using an incomplete solution of the subproblem
 SIAM Journal of Optimization
, 1995
"... Ary opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do NOT necessarily reflect the views of the above sponsors. ..."
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Cited by 31 (2 self)
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Ary opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do NOT necessarily reflect the views of the above sponsors.
Some theoretical properties of an augmented Lagrangian merit function
 in Advances in Optimization and Parallel Computing
, 1992
"... Sequential quadratic programming (SQP) methods for nonlinearly constrained optimization typically use a merit function to enforce convergence from an arbitrary starting point. We define a smooth augmented Lagrangian merit function in which the Lagrange multiplier estimate is treated as a separate v ..."
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Cited by 28 (7 self)
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Sequential quadratic programming (SQP) methods for nonlinearly constrained optimization typically use a merit function to enforce convergence from an arbitrary starting point. We define a smooth augmented Lagrangian merit function in which the Lagrange multiplier estimate is treated as a separate variable, and inequality constraints are handled by means of nonnegative slack variables that are included in the linesearch. Global convergence is proved for an SQP algorithm that uses this merit function. We also prove that steps of unity are accepted in a neighborhood of the solution when this merit function is used in a suitable superlinearly convergent algorithm. Finally, some numerical results are presented to illustrate the performance of the associated SQP method.
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 PRIMALDUAL AUGMENTED LAGRANGIAN
, 2008
"... Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primaldual generalization of the HestenesPowell augmented Lagrangi ..."
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Cited by 16 (2 self)
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Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primaldual generalization of the HestenesPowell augmented Lagrangian function. This generalization has the crucial feature that it is minimized with respect to both the primal and the dual variables simultaneously. A benefit of this approach is that the quality of the dual variables is monitored explicitly during the solution of the subproblem. Moreover, each subproblem may be regularized by imposing explicit bounds on the dual variables. Two primaldual variants of conventional primal methods are proposed: a primaldual bound constrained Lagrangian (pdBCL) method and a primaldual ℓ1 linearly constrained Lagrangian (pdℓ1LCL) method.
The Utility of Nonlinear Programming Algorithms: A Comparative Study, Part I & II ,"
 ASME JOURNAL OF MECHANICAL DESIGN,
, 1980
"... A comprehensive comparative study of nonlinear programming algorithms, as applied to problems in engineering design, is presented. Linear approximation methods, interior penalty and exterior penalty methods were tested on a set of thirty problems and are rated on their ability to solve problems wit ..."
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Cited by 10 (0 self)
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A comprehensive comparative study of nonlinear programming algorithms, as applied to problems in engineering design, is presented. Linear approximation methods, interior penalty and exterior penalty methods were tested on a set of thirty problems and are rated on their ability to solve problems within a reasonable amount of computational time. In this paper, we give and discuss numerical results and algorithm performance curves. Results Many attempts have been made at developing a relative ranking criterion for comparing nonlinear programming codes. These criteria have been based on different factors such as the number of problems solved or partially solved, some weighted average of execution times or the total running cost including input and output units, core usage and the estimated preparation time. The use of different rating criteria can significantly affect the relative rankings of the codes. This was demonstrated in the Eason and Fenton study where the relative rankings of the codes changed considerably depending upon which criterion was used. To avoid this problem careful consideration must be given to the characteristics a "good" code should possess. Certainly, the ability to solve problems must be considered to be the main characteristic of such a code, since this is the basic function of any nonlinear programming algorithm. This quality alone, however, does not represent the total value of a code. Given enough trials and enough computer time most codes will solve a fairly large set of problems. To generate a total picture of the relative effectiveness of a code, some consideration must be given to the computational time required for the solution of a test problem. The fact that one code solved a specific problem in seven seconds while another required fifteen seconds is not significant in itself, but if the same code consistently produces lower solution times, considerable time savings could result in general usage. This would especially be true for large scale problems or for problems where the objective function or constraints require a considerable amount of time to evaluate. Again, taken by itself, the relative solution time is not sufficient to comparatively rank codes, since a code which was extremely fast, but only solved a few problems, would rate well using this criterion. Thus, both the number of problems solved and the relative solution time must be considered in order to produce a valid indication of performance. University. Formerly graduate research asst., School of Mechanical Engineering, Purdue Contributed by the Design Automation Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received at ASME headquarters July, 1979. One method for dealing with multiple design objectives is to treat one as the major objective and all others as constraints. This was the approach used to develop the rating criterion to rank the algorithms in this study. Since the ability to solve a large number of problems in a reasonable amount of time is the desired ranking criterion, the rankings will be based on the number of problems solved within a series of specified limits on the relative solution times. The limits on the solution times will be based on a fraction of the average solution times for all of the codes on each problem. Each solution time for a problem was normalized by dividing by the average solution time on that problem. This produces a low normalized solution time for a code with a relatively fast solution time, and a high normalized solution time for a code with a relatively slow solution time. This normalization essentially equalizes the time ratings on the various problems. That is the relative effectiveness of a code on a problem which required a very small amount of time may be compared directly with the relative effectiveness on a problem which required a large amount of computational time. The number of problems solved may then be directly related to the fraction or percentage of the average solution time of all of the methods tested on each problem. The performance of the codes at various values of the fraction of average time will be considered for solutions at total error levels of 10~4, 10~5 and 10" 6 . It should be noted that problem 9, 13, 21, 22, 28, 29 and 30 were not included in this analysis since less than five algorithms generated the same solution point. A discussion of the results on these problems is given by Sandgren [1], Accordingly, we present results for 24 codes and 23 problems in our final results. With this background, consider the performance of the codes tested at a total error criterion of 10~4.
A new approach to optimization of chemical processes
 AlChE Journal
, 1980
"... A new approach to optimization of chemical processes ..."
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Cited by 9 (2 self)
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A new approach to optimization of chemical processes
Feasible Sequential Quadratic Programming For Finely Discretized Problems From Sip
, 1998
"... A Sequential Quadratic Programming algorithm designed to efficiently solve nonlinear optimization problems with many inequality constraints, e.g. problems arising from finely discretized SemiInfinite Programming, is described and analyzed. The key features of the algorithm are (i) that only a few o ..."
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Cited by 8 (1 self)
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A Sequential Quadratic Programming algorithm designed to efficiently solve nonlinear optimization problems with many inequality constraints, e.g. problems arising from finely discretized SemiInfinite Programming, is described and analyzed. The key features of the algorithm are (i) that only a few of the constraints are used in the QP subproblems at each iteration, and (ii) that every iterate satisfies all constraints. 1 INTRODUCTION Consider the SemiInfinite Programming (SIP) problem minimize f(x) subject to \Phi(x) 0; (SI) where f : IR n ! IR is continuously differentiable, and \Phi : IR n ! IR is defined by \Phi(x) \Delta = sup ¸2[0;1] OE(x; ¸); with OE : IR n \Theta [0; 1] ! IR continuously differentiable in the first argument. For an excellent survey of the theory behind the problem (SI), in addition to some algorithms and applications, see [9] as well as the other papers in the present volume. Many globally convergent algorithms designed to solve (SI) 2 Chapter 1...
A Simultaneous Solution Method Based on A Modular Approach for Power Plant Analyses and Optimized
 Designs and Operations,’’ International Gas Turbine and Aeroengine Congress and Exhibition
, 1996
"... !The Society shall not be responsible for statements or opinions advanced in Papers or discussion at meetings of the Society or of its DiVi$101113 or. Sections, or printed in its publications. Discussion is printed only if the paper is published in an ASME Journal. Authorization to photocopy.0 mate ..."
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Cited by 3 (1 self)
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!The Society shall not be responsible for statements or opinions advanced in Papers or discussion at meetings of the Society or of its DiVi$101113 or. Sections, or printed in its publications. Discussion is printed only if the paper is published in an ASME Journal. Authorization to photocopy.0 material for internal or personal use under circumstance not falling within the fair use provisions of the Copyright Act is granted by ASME to libraries and other users registered with the Copyright Clearance Center (CCC) Transactional Reporting Service provided that the base fee of