An optimizing control scheme is developed for multivariable constrained chemical processes. The scheme is based on a process model obtained from fundamental knowledge of the process to be controlled. The model is identified adaptively on-line and dynamic information from the model is used for on-line updating of the Internal Model Controller (IMC), which makes an adaptive IMC.Constrained steady state optimization is accomplished in an on-line application of Succesive Quadratic Programming (SQP) and is combined with the adaptive IMC. Our adaptive optimizing control scheme is tested on simulation studies. First, the development of the adaptive IMC scheme is described using SISO system and then the adaptive optimizing IMC scheme is described using MIMO system.