Projectionally exposed cones in R3
Projectionally exposed cones in R3
复制标题
R3 中的投影暴露锥体
DOI：
10.1016/0024-3795(88)90058-4
复制
发表时间：
1988
影响因子：
1.1
通讯作者：
M. Laidacker
中科院分区：
文献类型：
--
作者：
G. Poole;M. Laidacker
根据目标函数和约束类型，规划问题可以分为线性、非线性、离散、整数、布尔等，这些规划问题代表了以下更一般的抽象凸规划问题（ACPP）的特殊情况：求min {n（x）：g（x）∈− K，x∈ Ω}，其中Ω <$R n是凸的，K是凸锥，f，g是凸函数。ACPP的最优性刻画在最优化问题的研究中具有重要意义。Rn中的锥K称为投影暴露的，如果对于K的每个面F，存在Rn的投影PF，使得PF（K）= F。特别是，已经表明，当ACPP的约束函数g在投影暴露的圆锥中取值时，则可以从较小的集合中选择与最优性相关的某些乘数。本文完全刻划了R3的投影暴露锥.
Programming problems may be classified, on the basis of the objective function and types of constraints, as linear, nonlinear, discrete, integer, Boolean, etc. These programming problems represent special cases of the following more general abstract convex programming problem (ACPP): Find min {ƒ (x): g (x)∈− K, x∈ Ω}, where Ω⊆ R n is convex, K is a convex cone, and f, g are convex functions. Characterizations of optimality to the ACPP are of paramount importance in the investigation of optimization problems. A cone K in R n is called projectionally exposed if for each face F of K there exists a projection P F of R n such that P F (K)= F. In particular, it has been shown that when the constraint function g of the ACPP takes values in a projectionally exposed cone, then certain multipliers, associated with optimality, may be chosen from a smaller set. The projectionally exposed cones of R 3 are completely characterized in this paper.