Convex majorization methods for nonconvex constrained problems achieve O(ε^{-(κ+1)/κ}) iteration complexity under Hölderian gradients, with a second-order variant reaching approximate second-order stationarity in O(1/ε1+1/ε2) subproblem solves.
Safe Zeroth-Order Optimization Using Linear Programs
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
To solve unmodeled optimization problems with hard constraints, this paper proposes a novel zeroth-order approach called Safe Zeroth-order Optimization using Linear Programs (SZO-LP). The SZO-LP method solves a linear program in each iteration to find a descent direction, followed by a step length determination. We prove that, under mild conditions, the iterates of SZO-LP have an accumulation point that is also the primal of a KKT pair. We then apply SZO-LP to solve an Optimal Power Flow (OPF) problem on the IEEE 30-bus system. The results demonstrate that SZO-LP requires less computation time and samples compared to state-of-the-art approaches.
citation-role summary
background 1
citation-polarity summary
fields
math.OC 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
support 1representative citing papers
citing papers explorer
-
Complexity Analysis of Convex Majorization Schemes for Nonconvex Constrained Optimization
Convex majorization methods for nonconvex constrained problems achieve O(ε^{-(κ+1)/κ}) iteration complexity under Hölderian gradients, with a second-order variant reaching approximate second-order stationarity in O(1/ε1+1/ε2) subproblem solves.