### Abstract

This paper derives first order necessary and sufficient conditions for unconstrained cone d.c. programming problems where the underlined space is partially ordered with respect to a cone. These conditions are given in terms of directional derivatives and subdifferentials of the component functions. Moreover, conjugate duality for cone d.c. optimization is discussed and weak duality theorem is proved in a more general partially ordered linear topological vector space (generalizing the results in [11]).

Original language | English |
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Pages (from-to) | 521-528 |

Number of pages | 8 |

Journal | Chinese Annals of Mathematics. Series B |

Volume | 24 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2003 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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*Chinese Annals of Mathematics. Series B*, vol. 24, no. 4, pp. 521-528. https://doi.org/10.1142/S0252959903000529

**On cone d.c. optimization and conjugate duality.** / Semu, M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On cone d.c. optimization and conjugate duality

AU - Semu, M.

PY - 2003

Y1 - 2003

N2 - This paper derives first order necessary and sufficient conditions for unconstrained cone d.c. programming problems where the underlined space is partially ordered with respect to a cone. These conditions are given in terms of directional derivatives and subdifferentials of the component functions. Moreover, conjugate duality for cone d.c. optimization is discussed and weak duality theorem is proved in a more general partially ordered linear topological vector space (generalizing the results in [11]).

AB - This paper derives first order necessary and sufficient conditions for unconstrained cone d.c. programming problems where the underlined space is partially ordered with respect to a cone. These conditions are given in terms of directional derivatives and subdifferentials of the component functions. Moreover, conjugate duality for cone d.c. optimization is discussed and weak duality theorem is proved in a more general partially ordered linear topological vector space (generalizing the results in [11]).

UR - http://www.scopus.com/inward/record.url?scp=0347020813&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347020813&partnerID=8YFLogxK

U2 - 10.1142/S0252959903000529

DO - 10.1142/S0252959903000529

M3 - Article

AN - SCOPUS:0347020813

VL - 24

SP - 521

EP - 528

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

SN - 0252-9599

IS - 4

ER -