The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exac...The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.展开更多
The purpose of this paper is to devise exact l_(1) exponential penalty function method to solve multiobjective optimization problems with exponentialtype invexity.The conditions governing the equivalence of the(weak)...The purpose of this paper is to devise exact l_(1) exponential penalty function method to solve multiobjective optimization problems with exponentialtype invexity.The conditions governing the equivalence of the(weak)efficient solutions to the vector optimization problem and the(weak)efficient solutions to associated unconstrained exponential penalized multiobjective optimization problem are studied.Examples are given to illustrate the obtained results.展开更多
The objective of this paper is to propose an exact l1 penalty method for constrained interval-valued programming problems which transform the constrained problem into an unconstrained interval-valued penalized optimiz...The objective of this paper is to propose an exact l1 penalty method for constrained interval-valued programming problems which transform the constrained problem into an unconstrained interval-valued penalized optimization problem.Under some suitable conditions,we establish the equivalence between an optimal solution of interval-valued primal and penalized optimization problem.Moreover,saddle-point type optimality conditions are also established in order to find the relation between an optimal solution of penalized optimization problem and saddle-point of Lagrangian function.Numerical examples are given to illustrate the derived results.展开更多
文摘The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.
基金The research of the first author is financially supported by the University Grant Commission,New Delhi,India(No.41-801/2012(SR)).
文摘The purpose of this paper is to devise exact l_(1) exponential penalty function method to solve multiobjective optimization problems with exponentialtype invexity.The conditions governing the equivalence of the(weak)efficient solutions to the vector optimization problem and the(weak)efficient solutions to associated unconstrained exponential penalized multiobjective optimization problem are studied.Examples are given to illustrate the obtained results.
基金the Department of Science and Technology,New Delhi,India(No.SR/FTP/MS-007/2011).
文摘The objective of this paper is to propose an exact l1 penalty method for constrained interval-valued programming problems which transform the constrained problem into an unconstrained interval-valued penalized optimization problem.Under some suitable conditions,we establish the equivalence between an optimal solution of interval-valued primal and penalized optimization problem.Moreover,saddle-point type optimality conditions are also established in order to find the relation between an optimal solution of penalized optimization problem and saddle-point of Lagrangian function.Numerical examples are given to illustrate the derived results.
