A Data-embedded Solution Paradigm for Nonconvex Probable Event Constrained Optimization

Abstract

This paper introduces a new modeling framework for optimization under uncertainty, called Probable Event Constrained Optimization (PECO). Unlike conventional chance-constrained formulations, which only limit the probability of constraint violation, PECO also explicitly requires feasibility for all events whose probability exceeds a prescribed threshold. This guarantees that solutions remain valid across all high-probability realizations of uncertainty. To solve PECO, we proposed a data-embedded program (DEP) which directly incorporates historical measurements of the uncertain parameters to obtain a deterministic approximation for PECO. While existing solution methods for optimization problems under uncertainty rely heavily on convexity or linearity assumptions, the proposed data-embedded solution paradigm provides a unique opportunity for solving nonlinear and nonconvex PECOs. The effectiveness of this approach depends on properly estimating the number of elements in the family of solution-determining data sets. As we enter the era of big data, this information can be properly estimated by leveraging the power of machine learning.