Global optimality of the full robust nonlinear pricing program

Establish whether the full robust nonlinear pricing program admits globally optimal solutions or otherwise characterize and resolve its potential local-optima problem.

Background

The paper formulates spatially coupled parking pricing as a constrained nonlinear program with occupancy dynamics, price bounds, temporal price-change limits, neighbor price-gap constraints, and scenario-specific revenue floors. The program is solved using Ipopt with multiple starting points, but Ipopt is a local nonlinear optimization method and therefore does not by itself establish global optimality.

Small-instance comparisons against increment-grid candidates and agreement across multistart solutions provide empirical evidence about solution quality for selected deterministic instances. However, the paper explicitly leaves unresolved whether local-optima concerns persist for the full robust formulation, which includes uncertainty across demand scenarios and risk-sensitive objectives.