An SQP method for minimization of locally Lipschitz functions with nonlinear constraints
In this paper, we present a quadratic model for minimizing problems with nonconvex and nonsmooth objective and constraint functions. This method is based on sequential quadratic programming that uses an penalty function to equilibrate among the decrease of the objective function and the feasibility...
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| Vydané v: | Optimization Ročník 68; číslo 4; s. 731 - 751 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Philadelphia
Taylor & Francis
03.04.2019
Taylor & Francis LLC |
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| ISSN: | 0233-1934, 1029-4945 |
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| Abstract | In this paper, we present a quadratic model for minimizing problems with nonconvex and nonsmooth objective and constraint functions. This method is based on sequential quadratic programming that uses an
penalty function to equilibrate among the decrease of the objective function and the feasibility of the constraints. To construct a quadratic subproblem, we linearize the objective and constraint functions with their ε-subdifferential approximations. These approximations are iteratively improved until an effective descent direction is found. Also, we prove that our method is globally convergent in the sense that, every accumulation point of the generated sequence is a Clark-stationary point for the penalty function. Finally, the presented algorithm is implemented in Matlab environment and compared with some recent methods. |
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| AbstractList | In this paper, we present a quadratic model for minimizing problems with nonconvex and nonsmooth objective and constraint functions. This method is based on sequential quadratic programming that uses an
penalty function to equilibrate among the decrease of the objective function and the feasibility of the constraints. To construct a quadratic subproblem, we linearize the objective and constraint functions with their ε-subdifferential approximations. These approximations are iteratively improved until an effective descent direction is found. Also, we prove that our method is globally convergent in the sense that, every accumulation point of the generated sequence is a Clark-stationary point for the penalty function. Finally, the presented algorithm is implemented in Matlab environment and compared with some recent methods. In this paper, we present a quadratic model for minimizing problems with nonconvex and nonsmooth objective and constraint functions. This method is based on sequential quadratic programming that uses an [Formula omitted.] penalty function to equilibrate among the decrease of the objective function and the feasibility of the constraints. To construct a quadratic subproblem, we linearize the objective and constraint functions with their [epsilon]-subdifferential approximations. These approximations are iteratively improved until an effective descent direction is found. Also, we prove that our method is globally convergent in the sense that, every accumulation point of the generated sequence is a Clark-stationary point for the penalty function. Finally, the presented algorithm is implemented in Matlab environment and compared with some recent methods. |
| Author | Yousefpour, Rohollah Jafari, Elham |
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| SubjectTerms | Algorithms Approximation nonlinear constraint Penalty function Quadratic programming Sequential quadratic model ε-subdifferential |
| Title | An SQP method for minimization of locally Lipschitz functions with nonlinear constraints |
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