Multi-stage optimization for unit commitment considering dispatch non-anticipativity (DN) serves as a key approach to overcoming the operational risks in the day-ahead/real-time dispatch paradigm

and to ensuring the reliable operation of power systems with renewable energy integration under strong uncertain environment. Firstly

a DN-oriented multi-stage robust mixed-integer optimization model for unit commitment with piecewise mixed decision rules (PMDR) is advanced. Additionally

the structural properties of the PMDR-based model are analyzed

and

by integrating the proposed a priori theorem for identifying critically binding scenarios (CBSs) with the high-dimensional convex-hull equivalence construction

an efficient solution method—featuring warm-start strategies

the linear strong-duality paradigm

and an improved cutting-plane scheme—is subsequently developed. Numerical results

including a posteriori assessment on the augmented IEEE 39-bus test systems

demonstrate the effectiveness of the proposed model

solution method

and the a priori acquisition theorem of CBSs

while a broader analysis highlights its applicability across diverse research domains.