Sequential Convex Restriction and its Applications in Robust Optimization [article]

Dongchan Lee, Konstantin Turitsyn, Jean-Jacques Slotine
2019 arXiv   pre-print
This paper presents a convex sufficient condition for solving a system of nonlinear equations under parametric changes and proposes a sequential convex optimization method for solving robust optimization problems with nonlinear equality constraints. By bounding the nonlinearity with concave envelopes and using Brouwer's fixed point theorem, the sufficient condition is expressed in terms of closed-form convex inequality constraints. We extend the result to provide a convex sufficient condition
more » ... r feasibility under bounded uncertainty. Using these conditions, a non-convex optimization problem can be solved as a sequence of convex optimization problems, with feasibility and robustness guarantees. We present a detailed analysis of the performance and complexity of the proposed condition. The examples in polynomial optimization and nonlinear network are provided to illustrate the proposed method.
arXiv:1909.01778v1 fatcat:i3f7ra54ajewnevago7rproyoa