鲁棒线性最优化的若干扩展(英文)

Some Extensions of Robust Linear Optimization

本文基于凸锥理论对鲁棒线性最优化作了若干拓展。本文的拓展分为三部分。首先我们放松了对不确定集的限制,把鲁棒线性最优化拓展到凸锥和子空间平移的交的不确定集的情形。其次我们考虑了由凸不等式定义的不确定集的鲁棒线性最优化。再次,我们把鲁棒线性最优化拓展到了包含系数不确定性和解的实现误差的情形。对某些特殊的情形,我们导出了鲁棒线性最优化的确定性等价问题。

Based on theory of convex cones, our extensions of robust linear optimization are done in three directions. First, we relax the uncertainty set to be intersection of a closed convex cone and the translation of an affine subspace. Secondly, we consider the case that the uncertainty set is defined by convex functional inequalities. Thirdly, except for consid- ering uncertainty of the coefficients of a linear optimization model, we also incorporate implementation error of the obtained solution into the model. For some special cases, the deterministic convex optimization problems are derived.