A first order, exact penalty function algorithm for equality constrained optimization problems

1979 ◽  
Vol 16 (1) ◽  
pp. 303-324 ◽  
Author(s):  
D. Q. Mayne ◽  
N. Maratos
Keyword(s):  
Constrained Optimization ◽  
Penalty Function ◽  
Optimization Problems ◽  
Exact Penalty Function ◽  
Exact Penalty ◽  
Constrained Optimization Problems ◽  
First Order ◽  
Equality Constrained Optimization

scholarly journals A new auxiliary function approach for inequality constrained global optimization problems

2019 ◽  
Vol 9 (3) ◽  
pp. 31-38
Author(s):  
Nurullah Yilmaz ◽  
Ahmet Sahiner
Keyword(s):  
Global Optimization ◽  
Penalty Function ◽  
Optimization Problems ◽  
Auxiliary Function ◽  
Exact Penalty Function ◽  
Function Approach ◽  
Exact Penalty ◽  
Constrained Global Optimization ◽  
Constrained Optimization Problems ◽  
Smooth Exact Penalty Function

In this study, we deal with the nonlinear constrained global optimization problems. First, we introduce a new smooth exact penalty function for constrained optimization problems. We combine the exact penalty function with the auxiliary function in regard to constrained global optimization. We present a new auxiliary function approach and the adapted algorithm for solving  non-linear inequality constrained global optimization problems. Finally, we illustrate the efficiency of the algorithm on some numerical examples.

scholarly journals Composite Differential Evolution with Modified Oracle Penalty Method for Constrained Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Minggang Dong ◽  
Ning Wang ◽  
Xiaohui Cheng ◽  
Chuanxian Jiang
Keyword(s):  
Differential Evolution ◽  
Constrained Optimization ◽  
Penalty Function ◽  
Optimization Problems ◽  
Real Life ◽  
Optimization Criterion ◽  
Constrained Optimization Problems ◽  
Constraints Handling ◽  
Efficient Alternative ◽  
Handling Methods

Motivated by recent advancements in differential evolution and constraints handling methods, this paper presents a novel modified oracle penalty function-based composite differential evolution (MOCoDE) for constrained optimization problems (COPs). More specifically, the original oracle penalty function approach is modified so as to satisfy the optimization criterion of COPs; then the modified oracle penalty function is incorporated in composite DE. Furthermore, in order to solve more complex COPs with discrete, integer, or binary variables, a discrete variable handling technique is introduced into MOCoDE to solve complex COPs with mix variables. This method is assessed on eleven constrained optimization benchmark functions and seven well-studied engineering problems in real life. Experimental results demonstrate that MOCoDE achieves competitive performance with respect to some other state-of-the-art approaches in constrained optimization evolutionary algorithms. Moreover, the strengths of the proposed method include few parameters and its ease of implementation, rendering it applicable to real life. Therefore, MOCoDE can be an efficient alternative to solving constrained optimization problems.

scholarly journals A Nonmonotone Trust Region Algorithm Based on the Average of the Successive Penalty Function Values for Nonlinear Optimization

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Zhensheng Yu ◽  
Jinhong Yu
Keyword(s):  
Global Convergence ◽  
Penalty Function ◽  
Optimization Problems ◽  
Trust Region ◽  
Trust Region Methods ◽  
Constrained Optimization Problems ◽  
Trust Region Algorithm ◽  
Numerical Tests ◽  
Equality Constrained Optimization ◽  
Nonlinear Equality

We present a nonmonotone trust region algorithm for nonlinear equality constrained optimization problems. In our algorithm, we use the average of the successive penalty function values to rectify the ratio of predicted reduction and the actual reduction. Compared with the existing nonmonotone trust region methods, our method is independent of the nonmonotone parameter. We establish the global convergence of the proposed algorithm and give the numerical tests to show the efficiency of the algorithm.

Smoothing Approximation to the New Exact Penalty Function with Two Parameters

2021 ◽  
pp. 2140010
Author(s):  
Jing Qiu ◽  
Jiguo Yu ◽  
Shujun Lian
Keyword(s):  
Global Solution ◽  
Penalty Function ◽  
Original Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Exact Penalty ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Nonlinear Inequality ◽  
Two Parameters

In this paper, we propose a new non-smooth penalty function with two parameters for nonlinear inequality constrained optimization problems. And we propose a twice continuously differentiable function which is smoothing approximation to the non-smooth penalty function and define the corresponding smoothed penalty problem. A global solution of the smoothed penalty problem is proved to be an approximation global solution of the non-smooth penalty problem. Based on the smoothed penalty function, we develop an algorithm and prove that the sequence generated by the algorithm can converge to the optimal solution of the original problem.

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