Theory of linear and integer programming
Theory of linear and integer programming
Integer and combinatorial optimization
Integer and combinatorial optimization
A quantitative approach to logical inference
Decision Support Systems
An optimal k-consistency algorithm
Artificial Intelligence
Logic-based 0-1 constraint programming
Logic-based 0-1 constraint programming
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Logic-Based Methods for Optimization
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
A scheme for unifying optimization and constraint satisfaction methods
The Knowledge Engineering Review
An Integrated Solver for Optimization Problems
Operations Research
Duality in optimization and constraint satisfaction
CPAIOR'06 Proceedings of the Third international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
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Theconstraint programming community has recently begun to addresscertain types of optimization problems. These problems tend tobe discrete or to have discrete elements. Although sensitivityanalysis is well developed for continuous problems, progressin this area for discrete problems has been limited. This paperproposes a general approach to sensitivity analysis that appliesto both continuous and discrete problems. In the continuous case,particularly in linear programming, sensitivity analysis canbe obtained by solving a dual problem. One way to broaden thisresult is to generalize the classical idea of a dual to thatof an ’’inference dual,‘‘ which can be defined for any optimizationproblem. To solve the inference dual is to obtain a proof ofthe optimal value of the problem. Sensitivity analysis can beinterpreted as an analysis of the role of each constraint inthis proof. This paper shows that traditional sensitivity analysisfor linear programming is a special case of this approach. Italso illustrates how the approach can work out in a discreteproblem by applying it to 0-1 linear programming (linear pseudo-booleanoptimization).