Robust Conic Satisficing

Inspired by the principle of satisficing (Simon 1955), Long et al. (2021) propose an alternative framework for optimization under uncertainty, which we term as a robust model. Instead sizing uncertainty set in optimization, model is specified target objective with aim delivering solution that least impacted achieving target. At heart this framework, minimize level constraint violation all possible realizations within support set. Our based on function evaluates to optimal value standard conic problem, can be used wide range functions are convex decision variables but either or concave uncertain parameters. We derive exact semidefinite formulation when biconvex quadratic penalty and ellipsoidal. also show equivalence between more general problems classical adaptive linear models sets, where latter solved approximately using affine recourse adaptation. More importantly, complete recourse, reasonably chosen polyhedral function, reformulation safe approximations do not lead infeasible if above optimum obtained nominal problem minimized. Finally, extend our data-driven setting showcase modelling computational benefits over three numerical examples: portfolio selection, log-sum-exp lot-sizing problem.