Interior Proximal Algorithm for Quasiconvex Programming Problems and Variational Inequalities with Linear Constraints

Brito A.S.; da Cruz Neto J.X.; Lopes J.O.; Oliveira P.R.

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Interior Proximal Algorithm for Quasiconvex Programming Problems and Variational Inequalities with Linear Constraints

机译：拟凸规划问题和带线性约束的变分不等式的内部近似算法。

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In this paper, we propose two interior proximal algorithms inspired by the logarithmic-quadratic proximal method. The first method we propose is for general linearly constrained quasiconvex minimization problems. For this method, we prove global convergence when the regularization parameters go to zero. The latter assumption can be dropped when the function is assumed to be pseudoconvex. We also obtain convergence results for quasimonotone variational inequalities, which are more general than monotone ones.

机译：在本文中，我们提出了两种基于对数二次方近端方法的内部近端算法。我们提出的第一种方法是解决一般的线性约束拟凸最小化问题。对于这种方法，当正则化参数变为零时，我们证明了全局收敛。当函数被假定为伪凸时，可以放弃后一个假设。我们还获得了比单调更为普遍的拟单调变分不等式的收敛结果。

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《Journal of Optimization Theory and Applications》 |2012年第1期|共18页
作者
Brito A.S.; da Cruz Neto J.X.; Lopes J.O.; Oliveira P.R.;
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正文语种 eng
中图分类应用数学;
关键词
Proximal algorithm; Quasiconvex function; Quasiconvex linearly constrained problems; Quasimonotone operator; Variational inequalities;

机译：近似算法;拟凸函数;拟凸线性约束问题;拟单调算子;变分不等式;

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专利

1. Interior Proximal Algorithm for Quasiconvex Programming Problems and Variational Inequalities with Linear Constraints [J] . Brito A.S., da Cruz Neto J.X., Lopes J.O., Journal of Optimization Theory and Applications . 2012,第1期

机译：拟凸规划问题和带线性约束的变分不等式的内部近似算法。
2. A non-interior-point algorithm predictor-corrector algorithm for Variational Inequality Problem with equality linear constraints [J] . Xizhen HU, Chongchao HUANG, Aihua LUO, Przeglad Elektrotechniczny . 2013,第3B期

机译：具有等式线性约束的变分不等式问题的非内点算法预测器-校正器算法
3. Solving Variational Inequality Problems with Linear Constraints by a Proximal Decomposition Algorithm [J] . DEREN HAN, HONG K. LO Journal of Global Optimization . 2004,第1期

机译：用线性分解算法求解线性约束的变分不等式问题。
4. Study on Approximate Proximal Point Algorithms for Monotone Variational Inequalities [C] . Bingsheng He, Maijian Qian, Yumei Wang International Conference on Numerical Optimization and Numerical Linear Algebra . 2004

机译：单调变分不等式近似近端点算法研究
5. Primal-dual interior-point algorithms for linear programs with many inequality constraints. [D] . Winternitz, Luke Michael Blohm. 2010

机译：具有许多不等式约束的线性程序的原始对偶内点算法。
6. An Accelerated Proximal Gradient Algorithm for Singly Linearly Constrained Quadratic Programs with Box Constraints [O] . Congying Han, Mingqiang Li, Tong Zhao, 2013

机译：带盒约束的单线性约束二次程序的加速近距离梯度算法
7. Convergence and polynomiality of primal-dual interior-point algorithms for linear programming with selective addition of inequalities [O] . Alexander Engau, Miguel F. Anjos 2016

机译：基于双重内部点算法的联系方式和多项式，选择性添加不等式

Interior Proximal Algorithm for Quasiconvex Programming Problems and Variational Inequalities with Linear Constraints

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