The exterior penalty function was used to convert the constrained optimization problem
into unconstrained optimization problem which was the requirement of these pattern search methods.
By adding penalty terms to the objective function, the penalty function method can transform a constrained optimization problem
into an unconstrained one.
The proposed discriminant fusion strategy has two advantages: 1) fused data has the largest class discriminant owing to obtaining the fusion coefficients by solving a constrained optimization problem
created in the average margin criterion; 2) fusion coefficients are unique owing to they are equal to the elements of the eigenvector of one eigenvalue problem transformed by the above optimization problem.
Saddle-point equations arise when a constrained optimization problem
is solved by Lagrange multipliers.
The above constrained optimization problem
was converted into unconstrained one using exterior penalty function approach in the following form
The SFDD in the present study is also formulated as a constrained optimization problem
Therefore, we expressed our estimation problem as a constrained optimization problem
, and then by using its simplified form in different algorithms, we will determine the most appropriate method.
We develop a multigrid method for the resulting constrained optimization problem
Firstly for the solution of an Optimal Control problem need to change the constrained optimization problem
into a unconstrained problem and the consequential function is known as the Hamiltonian function denoted as H.
Methods like Particle Swarm Optimization and Genetic Algorithms are capable of solving almost all types of optimization problems but they require constraint handling strategies like Penalty Functions to convert the constrained optimization problem
into an unconstrained one (Chaudhry et.
Particle Swarm Optimization Method for Constrained Optimization Problems
, Intelligent Technologies - Theory and Applications: New Trends in Intelligent Technologies, pp: 214-220.
Conclusion: Numerical comparisons of the study have witnessed that the RABC found better solution to the unconstrained as well as constrained optimization problems
in comparison with other meta-heuristic optimizers.