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The variation problem associated with the solution of Dirac's relativisticelectron equation is reviewed here. Derivation of the min-max theorem isdiscussed. A new observation is that the spurious roots of negative energysatisfy a max-min theorem. The min-max principle (MMP) for solution of Diracequation, extendable to the Dirac-Fock case, is concisely reviewed. MMP fortwo-electron Dirac-Coulomb equation is discussed. The min-max theorem isphysically interpreted for both Dirac and Dirac-Coulomb problems. Applicationsof MMP are collated in tables. Associated theoretical and computationaldevelopments are outlined. Limitations of MMP are spelt out and recentmathematical developments are discussed.

A Review of the Min-Max Approach to the Solution of Relativistic Electron Wave Equation