Multiple Nonlinear Constraints Research Articles

Developing Centrifugal Compressor Train Optimization Models for Performance Evaluation

Recent advances in numerical optimization software now allow problems arising in the evaluation of complex centrifugal compressor train performance to be solved readily by machinery users. Analyses of compressor operations often require consideration of multiple nonlinear constraints involving pressure, temperature, flow rate, composition, and power. Based on these constraints, the operational boundaries of the machinery must be evaluated. Frequently operating points of greatest interest exist where one of the operational variables, such as flow rate, is maximized subject to operational constraints. A methodology is proposed that can be used to apply commercially available optimization software to problems of this type. A review of gas equation of state relationships needed to determine thermodynamic properties is provided, as well as methods for calculating compressor discharge pressure based on polytropic head and efficiency. Recycle control is considered and a model is proposed.

Proper efficiency and duality for a class of constrained multiobjective fractional optimal control problems containing arbitrary norms

We establish necessary and sufficient conditions for properly efficient solutions of a class of nonsmooth nonconvex optimal control problems with multiple fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Subsequently, we utilize these proper efficiency criteria to construct two multiobjective dual problems and prove appropriate duality theorems. Also, we specialize and discuss these results for a particular case of our principal problem which contains square roots of positivesemidefinite quadratic forms. As special cases of the main proper efficiency and duality results, this paper also contains similar results for control problems with multiple, fractional, and ordinary objective functions.

Proper efficiency and duality for a class of multiobjective fractional variational problems containing arbitrary norms

Necessary and sufficient conditions are established for properly efficient solutions of a class of nonsmooth nonconvex variational problems with multiple fractional objective functions and nonlinear inequality constraints. Based on these proper efficiency criteria. two multiobjective dual problems are constructed and appropriate duality theorems are proved. These proper efficiency and duality results also contain as special cases similar rcsults fer constrained variational problems with multiplei fractional. and conventional objective functions, which are particular cases of the main variational problem considered in this paper

Systems Reliability Subject to Multiple Nonlinear Constraints

A simple computational procedure has been developed for maximizing reliability of multistage parallel systems subject to multiple nonlinear constraints. It appears that the procedure can be applied to a variety of optimization problems with separable objective and multiple constraint functions.