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The semi-analytical solution for the natural frequencies and mode shapes are presented by incorporating the constraint conditions using the method of Lagrange multipliers.
First, a closed-loop system is formed by incorporating the constraint terms into the system's dynamic equation and then the observer is designed based on the resulting closed loop system.
By incorporating the constraint of main lobe maintenance with conventional LCMV constraints, the constraints of RMM-LCMV can be obtained.
In the literature of optimization problems, one of common practices is to reformulate a constrained optimization problem for a unconstrained problem by incorporating the constraint as a penalty term.
The distance distributions, P r), were obtained by Tikhonov regularization in the distance domain, incorporating the constraint P r) > 0. A homogeneous three-dimensional model for micelle samples and a homogeneous two-dimensional model for proteoliposomes and lipodisq nanoparticles samples were used for background correction.
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The solution for the natural frequencies and mode shapes are presented by incorporating the constraints using Lagrange multipliers.
Then, a GP model incorporating the constraints of system, resource, and AHP priority is formulated to select the best set of warehouses without exceeding the limited available resources.
In the penalty functions method, the constrained optimization problem is solved using unconstrained optimization method by incorporating the constraints into the objective function thus transforming it into an unconstrained problem.
The authors in [5] proposed an integrated model for analysing the interdependency of natural gas and power system security while incorporating the constraints of gas network into the optimal solution of security-constrained unit commitment.
However, most of the controller design methods can not incorporate the constraint that the input has to be positive.
To solve the optimization problem numerically, standard algorithms for an unconstrained version of nonlinear least-squares problems are modified to incorporate the constraint.
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