Objective To effectively handle constrained optimization problems containing equations and inequali-ties,and to strive for the penalty functions with better properties and simpler forms,and the efficient and fast al-gorithms.Methods A new type of penalty function was proposed to solve the equality constrained optimization problems.Results The properties of the new penalty function smoothness and accuracy were obtained through the proof.Meanwhile,the optimal solution was obtained by appropriately selecting the value of penalty parameters.Specifically,under the constraints of Mangasarian Fromovitz(M-F),it was proven that when the penalty param-eter was sufficiently large,the local minimum of the unconstrained optimization problem was also the local mini-mum of the original equality constrained optimization problem.Based on the proposed penalty function form,the corresponding penalty function algorithm was provided.The results of numerical experiments verified the feasibil-ity of the penalty function algorithm in solving equality constrained optimization problems.Conclusion The newly proposed penalty function form has better properties,able to effectively transform equality constrained optimiza-tion problems into unconstrained optimization problems easy to be solved by using penalty function algorithms,providing a new reference method for constrained optimization problems.
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