The authors show transition points in parametric semidefinite optimization are finite and give a numerical algebraic geometry algorithm to find nonlinearity intervals and transition points.
On the sensitivity of the optimal partition for parametric second-order conic optimization
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this paper, using an optimal partition approach, we study the parametric analysis of a second-order conic optimization problem, where the objective function is perturbed along a fixed direction. We characterize the notions of so-called invariancy set and nonlinearity interval, which serve as stability regions of the optimal partition. We then propose, under the strict complementarity condition, an iterative procedure to compute a nonlinearity interval of the optimal partition. Furthermore, under primal and dual nondegeneracy conditions, we show that a boundary point of a nonlinearity interval can be numerically identified from a nonlinear reformulation of the parametric second-order conic optimization problem. Our theoretical results are supported by numerical experiments.
citation-role summary
background 1
citation-polarity summary
fields
math.OC 1years
2019 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
On computing the nonlinearity interval in parametric semidefinite optimization
The authors show transition points in parametric semidefinite optimization are finite and give a numerical algebraic geometry algorithm to find nonlinearity intervals and transition points.