unconstrained optimization problem

unconstrained optimization problem

[¦ən·kən′strānd ‚äp·tə·mə′zā·shən ‚präb·ləm]
(mathematics)
A nonlinear programming problem in which there are no constraint functions.
References in periodicals archive ?
3) Solving the simplified problem by SUMT and BFGS: sequential unconstrained minimization technique (SUMT) is used to reformulate the constrained problem to the unconstrained one and then solving the unconstrained optimization problem. We adopt barrier method, one of the SUMT based method, to solve P5.
Under Assumption 1 one can solve the optimization problem in three steps: (i) initialization of the penalty parameters [[lambda].sub.i](l), (ii) solution of the unconstrained optimization problem, (iii) updating the penalty parameter [[lambda].sub.i](l + 1) that violates the constraint in (10).
Each vector forms a candidate solution to the unconstrained optimization problem. At each generation G, DE employs the mutation and crossover operations to produce a trial vector U* for each individual vector [N.sup.G.sub.iK], also called target vector, in the current population.
The basic idea of these methods is to change, modify or convert the constrained optimization problem into an unconstrained optimization problem by adding or subtracting a penalty value to or from the objective (Ashok and Chandrugupta, 2011).
In this paper, we consider the unconstrained optimization problem:
One way is by solving the unconstrained optimization problem defined in (12), and the other one is by heuristic.
This is a solution of the unconstrained optimization problem.
In this work, to solve our formulated constrained optimization problem we have converted it into an unconstrained optimization problem by penalty function technique.
To solve this problem, Lagrange multiplier technique is used that gives an unconstrained optimization problem:
In this way the constrained optimization problem is converted into unconstrained optimization problem, and DE can be directly applied to antenna synthesis without any modification.
By the penalty method, the formulas (1)-(4) can be transformed into an unconstrained optimization problem