### Abstract

This paper is concerned with an optimization-satisfaction problem to determine an optimal solution such that a certain objective function is minimized, subject to satisfaction conditions against uncertainties of any disturbances or opponents' decisions. Such satisfaction conditions require that plural performance criteria are always less than specified values against any disturbances or opponents' decisions. Therefore, this problem is formulated as a minimization problem with the constraints which include max operations with respect to the disturbances or the opponents' decision variables. A new computational method is proposed in which a series of approximate problems transformed by applying a penalty function method to the max operations within the satisfaction conditions are solved by usual nonlinear programming. It is proved that a sequence of approximated solutions converges to a true optimal solution. The proposed algorithm may be useful for systems design under unknown parameters, process control under uncertainties, general approximation theory, and strategic weapons allocation problems.

Original language | English |
---|---|

Pages (from-to) | 37-46 |

Number of pages | 10 |

Journal | Automatica |

Volume | 18 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1982 |

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### Keywords

- computational method
- Computer-aided design
- decision theory under uncertainty
- infinitely constrained nonlinear programming
- mathematical programming
- optimization
- parametric programming
- penalty function method
- satisfaction approach

### ASJC Scopus subject areas

- Control and Systems Engineering
- Electrical and Electronic Engineering

### Cite this

*Automatica*,

*18*(1), 37-46. https://doi.org/10.1016/0005-1098(82)90024-3

**A new solution to optimization-satisfaction problems by a penalty method.** / Shimizu, Kiyotaka; Aiyoshi, Eitaro.

Research output: Contribution to journal › Article

*Automatica*, vol. 18, no. 1, pp. 37-46. https://doi.org/10.1016/0005-1098(82)90024-3

}

TY - JOUR

T1 - A new solution to optimization-satisfaction problems by a penalty method

AU - Shimizu, Kiyotaka

AU - Aiyoshi, Eitaro

PY - 1982

Y1 - 1982

N2 - This paper is concerned with an optimization-satisfaction problem to determine an optimal solution such that a certain objective function is minimized, subject to satisfaction conditions against uncertainties of any disturbances or opponents' decisions. Such satisfaction conditions require that plural performance criteria are always less than specified values against any disturbances or opponents' decisions. Therefore, this problem is formulated as a minimization problem with the constraints which include max operations with respect to the disturbances or the opponents' decision variables. A new computational method is proposed in which a series of approximate problems transformed by applying a penalty function method to the max operations within the satisfaction conditions are solved by usual nonlinear programming. It is proved that a sequence of approximated solutions converges to a true optimal solution. The proposed algorithm may be useful for systems design under unknown parameters, process control under uncertainties, general approximation theory, and strategic weapons allocation problems.

AB - This paper is concerned with an optimization-satisfaction problem to determine an optimal solution such that a certain objective function is minimized, subject to satisfaction conditions against uncertainties of any disturbances or opponents' decisions. Such satisfaction conditions require that plural performance criteria are always less than specified values against any disturbances or opponents' decisions. Therefore, this problem is formulated as a minimization problem with the constraints which include max operations with respect to the disturbances or the opponents' decision variables. A new computational method is proposed in which a series of approximate problems transformed by applying a penalty function method to the max operations within the satisfaction conditions are solved by usual nonlinear programming. It is proved that a sequence of approximated solutions converges to a true optimal solution. The proposed algorithm may be useful for systems design under unknown parameters, process control under uncertainties, general approximation theory, and strategic weapons allocation problems.

KW - computational method

KW - Computer-aided design

KW - decision theory under uncertainty

KW - infinitely constrained nonlinear programming

KW - mathematical programming

KW - optimization

KW - parametric programming

KW - penalty function method

KW - satisfaction approach

UR - http://www.scopus.com/inward/record.url?scp=0019926605&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0019926605&partnerID=8YFLogxK

U2 - 10.1016/0005-1098(82)90024-3

DO - 10.1016/0005-1098(82)90024-3

M3 - Article

AN - SCOPUS:0019926605

VL - 18

SP - 37

EP - 46

JO - Automatica

JF - Automatica

SN - 0005-1098

IS - 1

ER -