# Penalty and Smoothing Methods for Convex Semi-Infinite Programming

##### Citations

54 citations

### Cites background from "Penalty and Smoothing Methods for C..."

...1 in [1] shows some particular cases where the set Ω0 is easily obtainable....

[...]

33 citations

31 citations

25 citations

##### References

5,933 citations

### "Penalty and Smoothing Methods for C..." refers background in this paper

...We recall here some basic notions about asymptotic cones and functions (for more details see, for instance, the books of Auslender and Teboulle [4], Rockafellar [24])....

[...]

...We recall here some basic notions about asymptotic cones and functions (for more details see, for instance, the books of Auslender and Teboulle [4] and of Rockafellar [24])....

[...]

2,948 citations

2,067 citations

1,560 citations

### "Penalty and Smoothing Methods for C..." refers methods in this paper

...Applied to LSIP, especially Cheney and Goldstein [10] and Kelley [15] turn out to be identical or mere modifications of the dual simplex method discussed above, so that they have similar properties and drawbacks....

[...]

...Supposing that F is 1 (as is generally the case in ordinary CSIP), we can use cutting-plane methods of Cheney and Goldstein [10], Kelley [15], Veinott [31], or Elzinga and Moore [11], and their variants (see, e.g., Reemtsen and Görner [22] for more references)....

[...]

...To avoid slow convergence, constraint dropping rules are again given under some conditions as strict convexity on F for Cheney and Goldstein [10] and Kelley [15]....

[...]

...Supposing that F is 1 (as is generally the case in ordinary CSIP), we can use cutting-plane methods of Cheney and Goldstein [10], Kelley [15], Veinott [31], or Elzinga and Moore [11], and their variants (see, e....

[...]

465 citations

### "Penalty and Smoothing Methods for C..." refers background in this paper

...In [9], Chen and Mangasarian provided a systematic way to generate elements of 1....

[...]