Support properties of a family of connected compact sets

Josef Nedoma

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 1, page 67-79
  • ISSN: 0862-7959

Abstract

top
A problem of finding a system of proportionally located parallel supporting hyperplanes of a family of connected compact sets is analyzed. A special attention is paid to finding a common supporting halfspace. An existence theorem is proved and a method of solution is proposed.

How to cite

top

Nedoma, Josef. "Support properties of a family of connected compact sets." Mathematica Bohemica 126.1 (2001): 67-79. <http://eudml.org/doc/248876>.

@article{Nedoma2001,
abstract = {A problem of finding a system of proportionally located parallel supporting hyperplanes of a family of connected compact sets is analyzed. A special attention is paid to finding a common supporting halfspace. An existence theorem is proved and a method of solution is proposed.},
author = {Nedoma, Josef},
journal = {Mathematica Bohemica},
keywords = {set family; supporting hyperplane; lexicographic optimization; polyhedral approximation; set family; supporting hyperplane; lexicographic optimization; polyhedral approximation},
language = {eng},
number = {1},
pages = {67-79},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Support properties of a family of connected compact sets},
url = {http://eudml.org/doc/248876},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Nedoma, Josef
TI - Support properties of a family of connected compact sets
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 1
SP - 67
EP - 79
AB - A problem of finding a system of proportionally located parallel supporting hyperplanes of a family of connected compact sets is analyzed. A special attention is paid to finding a common supporting halfspace. An existence theorem is proved and a method of solution is proposed.
LA - eng
KW - set family; supporting hyperplane; lexicographic optimization; polyhedral approximation; set family; supporting hyperplane; lexicographic optimization; polyhedral approximation
UR - http://eudml.org/doc/248876
ER -

References

top
  1. Linear programming and extensions, Princeton University Press, Princeton, 1973. (1973) MR1658673
  2. Linear inequalities and related systems, Princeton University Press, Princeton, 1956. (1956) 
  3. 10.1287/opre.24.4.783, Oper. Res. 24 (1976), 783–787. (1976) Zbl0335.90035MR0437008DOI10.1287/opre.24.4.783
  4. 10.1080/02331939708844325, Optimization 41 (1997), 57–69. (1997) MR1460220DOI10.1080/02331939708844325
  5. On a calculation of an arbitrary separating hyperplane of convex polyhedral sets, Optimization 43 (1997), 93–112. (1997) MR1638843
  6. Separating support syperplanes for a pair of convex polyhedral sets, Optimization 43 (1997), 113–143. (1997) MR1638847
  7. On a supporting hyperplane for two convex polyhedral sets, Optimization 43 (1997), 235–255. (1997) MR1774340
  8. Separation and support properties of convex sets—A survey. In: A. V. Balakrishnan (ed.): Control Theory and the Calculus of Variations, Academic Press, New York, 1969. (1969) MR0394357
  9. Introduction to linear and nonlinear programming, Addison-Wesley Publishing Comp., 1973. (1973) Zbl0297.90044
  10. Numerische Methoden der Approximation und semi-infiniten Optimierung, Teubner, Stuttgart, 1982. (1982) MR0653476
  11. Semi-infinite programming, theory, methods and applications, SIAM Review 35, 380–429. MR1234637
  12. Linear independence and total separation of set families, Ekonomicko-matematický obzor 14 (1978). (1978) Zbl0422.15015MR0508972
  13. 10.1007/BF02023110, Ann. Oper. Res. 47 (1993), 483–496. (1993) Zbl0793.90033MR1260033DOI10.1007/BF02023110
  14. 10.1080/03081089808818545, Linear and Multilinear Algebra 44 (1998), 29–44. (1998) MR1638938DOI10.1080/03081089808818545
  15. Positively regular vague matrices, (to appear). (to appear) Zbl1002.15020MR1815951
  16. On the solution set of a linear system with inaccurate coefficients, SIAM J. Numer. Anal. 2 (1965), 115–118. (1965) Zbl0146.13404MR0178567
  17. 10.1007/BF01386090, Numer. Math. 6 (1964), 405–409. (1964) MR0168106DOI10.1007/BF01386090
  18. Linear programming with inexact coefficients, Res. Report, Japan Adv. Inst. Sci. Techn., Hokuriku, 1997. (1997) 
  19. Convex analysis, Princeton University Press, Princeton, 1970. (1970) Zbl0193.18401MR0274683
  20. Systems of linear interval equations, Linear Algebra Appl. 126 (1989), 39–78. (1989) Zbl0712.65029MR1040771
  21. Convexity and optimization in finite dimensions I, Springer, Berlin, 1970. (1970) MR0286498
  22. Connections between generalized, inexact and semi-infinite linear programming, ZOR-Methods Models Oper. Res. 33 (1989), 367–382. (1989) MR1030790
  23. 10.1287/opre.28.4.1005, Operations Research 28 (1980), 1005–1011. (1980) Zbl0441.90056MR0584904DOI10.1287/opre.28.4.1005

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.