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On the sensitivity of the optimal partition for parametric second-order conic optimization
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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.
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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.
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