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Presented in this document is a short discussion on using IMPL’s SLPQPE algorithm to solve process optimization problems in either off- or on-line environments also known as real-time optimization (RTO). Process optimization is somewhat different than production optimization in the sense that there are more “constitutive relations” involving only intensive variables. Both types of optimizations involve “conservation laws” and “correlative equations” which usually involve a mix of extensive and intensive variables (Kelly, 2004). Whereas production optimization deals more with material, meta-material (nonlinear), logic and logistics (discrete) balances (Zyngier and Kelly, 2009 and Kelly and Zyngier, 2015), process optimization is inherently more detailed and includes energy, exergy, momentum, hydraulics, equilibrium, diffusion, kinetics and other types of transport phenomena which involve nonlinear and perhaps discontinuous functions (Pantelides and Renfro, 2012).