Convergence Analysis of a Class of Nonlinear Penalization Methods for Constrained Optimization via First-Order Necessary Optimality Conditions |
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Authors: | XX Huang XQ Yang |
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Affiliation: | (1) Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing, China;(2) Present address: Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong |
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Abstract: | We propose a scheme to solve constrained optimization problems by combining a nonlinear penalty method and a descent method. A sequence of nonlinear penalty optimization problems is solved to generate a sequence of stationary points, i.e., each point satisfies a first-order necessary optimality condition of a nonlinear penalty problem. Under some conditions, we show that any limit point of the sequence satisfies the first-order necessary condition of the original constrained optimization problem. |
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Keywords: | Nonlinear penalization necessary optimality conditions differentiability locally Lipschitz functions smooth approximate variational principle |
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