Technical Note—A Note on the Application of Nonlinear Programming to Chemical-Process Optimization

1974

AIChE Journal

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In the optimization of engineering systems, constraints are frequently encountered in the form of equalities as well as inequalities. In many instances, the equality constraints can be readil handled simply by solving for a simple rearrangement is not possible has not received adequate attention in the literature. An equality which does not allow one variable to be solved readily in terms of the other variables is termed a dilqicult equality. The purpose of this note is to present an effective procedure to handle difficult equality constraints in nonlinear programming problems. (1) with the hyperboloidand consider the problem of determining the maximum distance from the origin to the intersection of the ellipsoid with the hyperboloid. We may consider the square of the distance and thus formulate the problem as the maximization of ( 3 ) subject to the constraints of Equations (1) and ( 2 ) . To keep the problem as simple as possible to visualize, no inequality constraints are added.The constraints given by Equations (1)

Section: Discussionmentioning

confidence: 94%

Two‐pass method for handling difficult equality constraints in optimization

1974

AIChE Journal

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“…Furthermore, the use of only a section of the data keeps the computation time reasonably small, even though a larger number of function evaluations are done at each iteration. The listing of the LJ optimization program has been given by Jaakola and Luus (1974), and therefore, no detailed comments about the minimization procedure are necessary. It is noted, however, that it is unnecessary to integrate the equations for the entire portion of the data chosen for each set of parameter values.…”

Section: Procedures For Good Initial Estimatesmentioning

confidence: 99%

Simplification of quasilinearization method for parameter estimation

Kalogerakis

1983

AIChE Journal

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“…k = lo), increment 1 by 1. A heavier penalty where p = 1.5' is used instead of equation (8). Set k = 0, go to step 4 and continue.…”

Section: At X' ( O )mentioning

confidence: 99%

Optimization of non‐unimodal systems

Wang

Numerical Meth Engineering

1977

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SUMMARYTwo direct search algorithms for the optimization of non-unimodal systems are presented. One method is interior in nature by using boundary relaxation with pseudo one-dimensional search in the feasible region; the other one is an exterior method which allows the violation of constraints followed by the use of a penalty function to drive the search back into the feasible region. These two methods are usually capable of leaving local optima to reach a better solution if such exists. The application of the proposed approaches to several non-unimodal systems shows that they are better than the existing methods. The proposed methods are also attractive because of the ease of programming and the high probability of reaching the global optimum.