A merit function for inequality constrained nonlinear programming
                        problems

Boggs, Paul T.; Tolle, Jon W.; Kearsley, Anthony J.

doi:10.6028/nist.ir.4702

Cited by 6 publications

(12 citation statements)

References 5 publications

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“…This can be the case with control problems governed by partial di erential equations (see 29] or 30]). If the partial di erential equation is solved using a nite element method, with piecewise linear elements, then evaluating the derivative of the objective Parameter Value M 10 minf10 7 ; krf(x 0 )k 1 minf10 3…”

Section: Numerical Results the Modi Ed Algorithm Was Coded In Fortramentioning

confidence: 99%

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A Practical Algorithm for General Large Scale Nonlinear Optimization Problems

Boggs¹,

Kearsley²,

Tolle³

1999

SIAM J. Optim.

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We provide an e ective and e cient implementation of a sequential quadratic programming (SQP) algorithm for the general large scale nonlinear programming problem. In this algorithm the quadratic programming subproblems are solved by an interior point method that can be prematurely halted by a trust region constraint. Numerous computational enhancements to improve the numerical performance are presented. These include a dynamic procedure for adjusting the merit function parameter and procedures for adjusting the trust region radius. Numerical results and comparisons are presented.

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Section: Numerical Results the Modi Ed Algorithm Was Coded In Fortramentioning

confidence: 99%

“…n). is a set of observed data, X is a con guration of atoms (their locations in R 3 , and D is a transformation into the space of \distance matrices". The bound matrices a; b are upper and lower bounds based on estimating errors in measurements.…”

Section: Numerical Results the Modi Ed Algorithm Was Coded In Fortramentioning

confidence: 99%

A Practical Algorithm for General Large Scale Nonlinear Optimization Problems

Boggs¹,

Kearsley²,

Tolle³

1999

SIAM J. Optim.

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“…In [BogTK91] we derived a merit function for (NLP) based on the work in [BogT84] and [BogT89] for equality constrained problems. This was done by considering the slack variable problem (see [Tap80])…”

Section: The Merit Functionmentioning

confidence: 99%

“…Thus we employ an approximate merit function and a globalization strategy that overcome these deficiencies. We use = /(®) + c(z, 2 )'^A*= +^c (x,z).4*=c (i,z) where We show in [BogTK91] that (S^, q^) is a descent direction for V'd everywhere, that will not interfere with rapid local convergence, and that the globalization strategy described in §4 is effective. The main theoretical result described here is that OSD and the merit function are compatible.…”

Section: The Merit Functionmentioning

confidence: 99%

“…(See e.g., [BogT89] and [BogTK9l].) In a previous paper, [BogTK91], the authors introduced a merit function for {NLP) and showed that it is appropriate for use with the SQP algorithm. In this paper we apply these ideas to the large scale case, solving {QP) only approximately by an iterative interior-point algorithm that we can stop prematurely.…”

Section: Introductionmentioning

confidence: 99%

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A truncated SQP algorithm for large scale nonlinear programming problems

Boggs¹,

Toll²,

Kearsley³

1992

Self Cite

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We consider the inequality constrained nonlinear programming problem and an SQP algorithm for its solution. We are primarily concerned with two aspects of the general procedure, namely, the approximate solution of the quadratic program, and the need for an appropriate merit function. We first describe an (iterative) interior-point method for the quadratic programming subproblem that, no matter when it its terminated, yields a descent direction for a suggested new merit function. An algorithm based on ideas from trust-region and truncated Newton methods, is suggested and some of our preliminary numerical results are discussed. '.?«1

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Sequential Quadratic Programming

1995

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Since its popularization in the late 1970s, Sequential Quadratic Programming (SQP) has arguably become the most successful method for solving nonlinearly constrained optimization problems. As with most optimization methods, SQP is not a single algorithm, but rather a conceptual method from which numerous specific algorithms have evolved. Backed by a solid theoretical and computational foundation, both commercial and public-domain SQP algorithms have been developed and used to solve a remarkably large set of important practical problems. Recently large-scale versions have been devised and tested with promising results.

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A merit function for inequality constrained nonlinear programming problems

Cited by 6 publications

References 5 publications

A Practical Algorithm for General Large Scale Nonlinear Optimization Problems

A Practical Algorithm for General Large Scale Nonlinear Optimization Problems

A truncated SQP algorithm for large scale nonlinear programming problems

Sequential Quadratic Programming

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