记录Primal-Dual Interior-Point Methods(PDIPM以下简称IPM)。并将和罚函数方法一起比较分析。 处理如下标准问题: minxf(x)subject tohi(x)≤0,i=1,…mAx=b 回顾barrier method: minxtf(x)+ϕ(x)s.t.Ax=b 其中采用对数障碍函数:ϕ(x)=−∑i=1mlog(
A primal-dual interior point method(IPM) not only is the most efficient method for a computational point of view but also has polynomial complexity. Most of polynomial-time interior point methods(IPMs) are based on the logarithmic barrier functions. Peng et al.([14, 15]) and Roos et al....
However, delivering the worst-case complexity analysis for an IPM with such updates is not straightforward, even for a single update. Equation (8) is the basis of the analysis developed in this work. It states that we can study quasi-Newton steps using the Jacobian of the Newton step. The...
These simple but interesting properties of the proximity function indicate that, when the current iterate is in a large neighborhood of the central path, then the large-update IPM emerges to be the only natural choice. Then, we apply these results to design a specific self-regularity based IPM...
SinceKarmarkar(1984)presentedaneficientinterior—pointmethod(IPM)forLO,L0has revivedasanactiveareaofresearch.ThevariantsofIPMsforLOhavebeensuccessfully extendedtokindsofmathematicalproblems,suchasconvexquadraticoptimization(CQO), complementarityproblem(CP),semi—definiteoptimization(SDO)andsoon.Itiswellknown R ec...
5) primal-dual interior point method (PDIPM) 原–对偶内点法(PDIPM) 6) primal-dual interior point method 原始-对偶内点法 补充资料:不动点算法 又称固定点算法。所谓不动点,是指将一个给定的区域A,经某种变换??(x),映射到A时,使得x=??(x)成立的那种点。最早出现的不动点理论是布劳威尔定理(1912...
Based on predictor-corrector interior point method (PCIPM) and improved genetic algorithm (IGA), a combination strategy for reactive power optimization is proposed, which divides reactive power optimization problem into two sub-problems, i. 提出了一种求解无功优化问题的组合策略,该策略将无功优化问题分...
In this paper, we propose a new IPM for semidefinite optimization (SDO) based on a parameterized kernel function which is a generalization of the one presented by Bai et al. (Optim Methods Softw 17(6):985鈥 1008, 2002). By using the good properties of the parameterized kernel function, ...
These simple but interesting properties of the proximity function indicate that, when the current iterate is in a large neighborhood of the central path, then the large-update IPM emerges to be the only natural choice. Then, we apply these results to design a specific self-regularity based IPM...
In this paper, we propose a path-following interior-point method (IPM) for solving linear optimization (LO) problems based on a new kernel function (KF). The latter differs from other KFs in having an exponential-hyperbolic barrier term that belongs to the hyperbolic...