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A BFGS-IP algorithm for solving strongly convex optimization problems with feasibility enforced by an exact penalty approach

机译:一种BFGS-IP算法,用于解决强凸优化问题,并具有通过精确罚分法强制执行的可行性

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摘要

This paper introduces and analyses a new algorithm for minimizing a convex function subject to a finite number of convex inequality constraints. It is assumed that the Lagrangian of the problem is strongly convex. The algorithm combines interior point methods for dealing with the inequality constraints and quasi-Newton techniques for accelerating the convergence. Feasibility of the iterates is progressively enforced thanks to shift variables and an exact penalty approach. Global and q-superlinear convergence is obtained for a fixed penalty parameter; global convergence to the analytic center of the optimal set is ensured when the barrier parameter tends to zero, provided strict complementarity holds.
机译:本文介绍并分析了一种新算法,该算法可在有限数量的凸不等式约束下使凸函数最小化。假定问题的拉格朗日是强凸的。该算法结合了用于处理不等式约束的内点方法和用于加速收敛的准牛顿技术。由于移位变量和精确的罚分方法,迭代的可行性逐渐得到加强。对于固定惩罚参数,获得了全局和q超线性收敛。当障碍参数趋于零时,只要严格的互补性成立,就能确保全局收敛到最优集的分析中心。

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