Infinite programming and theorems of the alternative
In this paper, we obtain optimal versions of the Karush–Kuhn–Tucker, Lagrange multiplier, and Fritz John theorems for a nonlinear infinite programming problem where both the number of equality and inequality constraints is arbitrary. To this end, we make use of a theorem of the alternative for a fam...
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| Published in | Mathematical methods in the applied sciences Vol. 42; no. 17; pp. 5769 - 5778 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Freiburg
Wiley Subscription Services, Inc
30.11.2019
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0170-4214 1099-1476 |
| DOI | 10.1002/mma.5566 |
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| Abstract | In this paper, we obtain optimal versions of the Karush–Kuhn–Tucker, Lagrange multiplier, and Fritz John theorems for a nonlinear infinite programming problem where both the number of equality and inequality constraints is arbitrary. To this end, we make use of a theorem of the alternative for a family of functions satisfying a certain type of weak convexity, the so‐called infsup‐convexity. |
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| AbstractList | In this paper, we obtain optimal versions of the Karush–Kuhn–Tucker, Lagrange multiplier, and Fritz John theorems for a nonlinear infinite programming problem where both the number of equality and inequality constraints is arbitrary. To this end, we make use of a theorem of the alternative for a family of functions satisfying a certain type of weak convexity, the so‐called infsup‐convexity. |
| Author | Montiel López, Pablo Ruiz Galán, Manuel |
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| Cites_doi | 10.2140/pjm.1958.8.171 10.1007/s10898-017-0525-x 10.1137/100817061 10.1080/02331930903552473 10.1023/A:1021781308794 10.1007/978-1-4684-9369-6 10.1007/s10479-014-1539-0 10.1007/BF02190126 10.1515/9781400873173 10.1007/978-3-642-21114-0_2 10.1007/s10957-013-0456-8 10.1007/s10898-015-0379-z 10.1155/2014/453912 10.1007/BF00934081 10.1007/s10957-016-0959-1 10.1016/j.na.2010.09.066 10.1016/j.hm.2003.07.001 10.1007/978-0-387-74759-0_371 10.4153/CMB-2012-028-5 10.1525/9780520411586-036 10.1007/BF01448847 10.1016/0022-247X(88)90054-6 10.1016/j.jmaa.2017.06.007 10.2307/1911819 10.1080/0233193021000031615 10.1073/pnas.39.1.42 |
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| References | 2014; 217 1982; 38 1953; 39 2012 2017; 69 2002; 51 2011; 60 1928; 100 2009 1953 2011; 74 1975 1951 2014; 2014 2004; 2 1970 1999; 101 1996; 91 2016; 17 1939 2017; 455 1958 1957 2014; 21 2004; 31 2016; 1 2016; 65 1958; 8 2014; 57 1988; 132 2014; 161 2016; 170 2011; 49 1948 1961; 29 e_1_2_6_32_1 Fenchel W (e_1_2_6_2_1) 1953 e_1_2_6_10_1 e_1_2_6_30_1 Stefanescu A (e_1_2_6_22_1) 2004; 2 Ruiz Galán M (e_1_2_6_26_1) 2014; 21 e_1_2_6_19_1 Ruiz Galán M (e_1_2_6_24_1) 2016; 17 e_1_2_6_13_1 e_1_2_6_14_1 e_1_2_6_35_1 e_1_2_6_11_1 Flores‐Bazán F (e_1_2_6_21_1) 2012 e_1_2_6_34_1 e_1_2_6_12_1 e_1_2_6_33_1 e_1_2_6_17_1 e_1_2_6_18_1 e_1_2_6_15_1 e_1_2_6_20_1 Uzawa H (e_1_2_6_31_1) 1958 e_1_2_6_9_1 e_1_2_6_8_1 Ruiz Galán M (e_1_2_6_16_1) 2016; 1 e_1_2_6_5_1 e_1_2_6_4_1 e_1_2_6_7_1 e_1_2_6_6_1 e_1_2_6_25_1 e_1_2_6_3_1 e_1_2_6_23_1 John F (e_1_2_6_36_1) 1948 e_1_2_6_29_1 e_1_2_6_28_1 e_1_2_6_27_1 |
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| SubjectTerms | Convexity infsup‐convexity Lagrange multiplier Nonlinear programming Theorems theorems of the alternative |
| Title | Infinite programming and theorems of the alternative |
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