A second-derivative SQP method with a `trust-region-free' predictor step (Q2882358)
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scientific article; zbMATH DE number 6030231
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A second-derivative SQP method with a `trust-region-free' predictor step |
scientific article; zbMATH DE number 6030231 |
Statements
4 May 2012
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nonlinear programming
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nonlinear inequality constraints
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sequential quadratic programming
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\(\ell_{1}\)-penalty function
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nonsmooth optimization
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global and local superlinear convergence
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numerical experiments
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A second-derivative SQP method with a `trust-region-free' predictor step (English)
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The authors consider the solution of the problem NEWLINE\[NEWLINE\underset{x\in \mathbb{R}^n}{}{\text{minimize}}\;\phi(x)= f(x)+ \sigma\|[c(x)^-\|,NEWLINE\]NEWLINE where \(\sigma\) is a positive scalar known as the penalty parameter and \([c(x)]= \min(0,c(x))\) and prove that a second-derivative sequential quadratic programming method is globally and locally superlinear convergent under common assumptions.NEWLINENEWLINE Solutions of this problem correspond under certain assumptions to solutions of the nonlinear programming problem NEWLINE\[NEWLINE\underset{x\in \mathbb{R}^n}{}{\text{minimize}}\;f(x)\quad\text{subject to }c(x)\geq 0.NEWLINE\]NEWLINE Numerical experiments are given.
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