| 非线性等式与不等式约束最优化二阶与超线性收敛的序列线性方程组算法 |
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| 引用本文： | 简金宝. 非线性等式与不等式约束最优化二阶与超线性收敛的序列线性方程组算法[J]. 应用基础与工程科学学报, 1996, 0(3) |
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| 作者姓名： | 简金宝 |
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| 作者单位： | 广西大学数学与信息科学系 南宁 |
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| 基金项目： | 中国科学院资助项目，亚太运筹学会亚太运筹中心资助项目 |
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| 摘 要： | 讨论非线性等式与不等式约束最优化问题,建立了问题的似Newton和拟Newton算法。算法的特点之一是搜索方向d_k仅由一个线性方程组的解确定,步长恒取1,即x_(k 1)=x_k d_k。另一特点是在没有严格互补的较温和的假设下,算法是二阶与超线性收敛的。本文推广了Facchinei,Lucidi,Boggs,Tolle,Wang等人的算法和收敛性结果。
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| 关 键 词： | 非线性等式与不等式 约束最优化问题 序列线性方程组 算法 超线性收敛性 |
Quadratically and Superlinearly Convergent Algorithms for Equality and Inequality Constrained Optimization Based on Solutions of Successive Linear Equations |
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| JIAN Jinbao. Quadratically and Superlinearly Convergent Algorithms for Equality and Inequality Constrained Optimization Based on Solutions of Successive Linear Equations[J]. Journal of Basic Science and Engineering, 1996, 0(3) |
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| Authors: | JIAN Jinbao |
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| Abstract: | In this paper, the optimization problems with nonlinearly equality and inequality constraints are discussed, and the Newton-like and quasi-Newtoh algorithms for this problems are pressented. One of the features of these algorithms is that the search directions are ditermined by only the solutions of linear equations, the step-length always equals one, i. e. , xt 1 = xk dk. The other feature is that these algorithms are quadratically and superlinearly convergent under mild assumptions which do not imply the strict complementarity condition. This paper generalizes the algorithms and convergent results of Facchinei-Lucidi, Boggs-Toll-Wang. |
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| Keywords: | nonlinearly equality and inequality constrained optimization problems successive linear equations algorithms superlinear convergence |
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