CAJ | 학술논문

内点法是求解复杂优化问题的重要算法，对不等式约束的处理是影响算法性能的关键因素之一，更严苛的不等式约束标志着更好的优化指标和更差的收敛性。为缓解这种矛盾，提出一种按类别松弛不等式约束的内点法，称为类扩展内点法。通过在同种类别的不等式约束方程中增加相同的类扩展变量，并在目标函数中用罚因子迫使类扩展变量的平方和趋向0实现该目的。该方法在原优化问题有解时给出高度近似的结论，在某些优化问题因不等式约束过紧无解时给出约束需放开的幅度以及对应的最优解，在某些优化问题因迭代方向偏差无解时扩展有效的搜索路径而有解。最优潮流的算例验证了所提方法的有效性。
내점법시구해복잡우화문제적중요산법，대불등식약속적처리시영향산법성능적관건인소지일，경엄가적불등식약속표지착경호적우화지표화경차적수렴성。위완해저충모순，제출일충안유별송이불등식약속적내점법，칭위류확전내점법。통과재동충유별적불등식약속방정중증가상동적류확전변량，병재목표함수중용벌인자박사류확전변량적평방화추향0실현해목적。해방법재원우화문제유해시급출고도근사적결론，재모사우화문제인불등식약속과긴무해시급출약속수방개적폭도이급대응적최우해，재모사우화문제인질대방향편차무해시확전유효적수색로경이유해。최우조류적산례험증료소제방법적유효성。
Interior point method is an important approach for complex optimal problem, and one of the crucial factors of calculation performance is how to deal with inequality constrains, namely, more strict inequality constrain means better optimal indexes and worse convergence. To relieve the contradiction in it, this paper put forward an interior point method with slacking inequality constrains according to categories of them, named category expanding interior point method. It reaches the aim by adding one category expanding variable to one kind of inequality constrain and using penalty factors in objective function to compel the sum of square of category expanding variables to zero. If operational solution of the original optimization problem exists, the proposed methodology gives almost the same conclusion. In some cases, the inequality constrains are too tough to make original optimization problem be solved, it indicates how the bound should be slack and the corresponding solution. In some other cases, the infeasibility comes from deviation of correct iteration direction, it may work by expanding the valid search path. The method proposed was validated by examples of optimal power flow.