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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
The optimal solution set of interval linear programming problems
 Garajová, Elif ; Hladík, Milan (advisor) ; Zimmermann, Karel (referee)
Determining the set of all optimal solutions of a linear program with interval data is one of the main problems discussed in interval optimization. We review two methods based on duality in linear programming, which are used to approximate the optimal set. Additionally, another decomposition method based on complementary slackness is proposed. This method provides the exact description of the optimal set for problems with a fixed coefficient matrix. The second part of the thesis is focused on studying the topological and geometric properties of the optimal set. We examine sufficient conditions for closedness, boundedness, connectedness and convexity. We also prove that testing boundedness is co- NP-hard for inequality-constrained problems with free variables. Stronger results are derived for some special classes of interval linear programs, such as problems with a fixed coefficient matrix. Furthermore, we study the effect of transformations commonly used in linear programming on interval problems, which allows for a direct generalization of some results to different types of interval linear programs. Powered by TCPDF (www.tcpdf.org)
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Duality in interval linear programming
 Novotná, Jana ; Hladík, Milan (advisor) ; Bartl, David (referee)
This thesis combines a traditional concept of linear programming and interval analysis. Interval analysis ensures that a result belongs to a counted interval and allows us to put an interval instead of a single value on the input. It can be useful especially in practical problems where we get data from measurements and we do not know exact values. The first explored topic is the optimal value range with respect to values and its bounds. Also, the classical concept of duality gap is expanded to interval linear programmimg, necessary and sufficient conditions for zero duality gap and connections between zero duality gap and a continuous set of optimal values are determined. Possible values of duality gap in an interval linear program are shown in examples. The last topic are weak and strong duality in interval linear programming, strong duality types for bounds of the optimal value range and their extensions. Powered by TCPDF (www.tcpdf.org)
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