A Rigorous Lower Bound for the Optimal Value of Convex Optimization Problems
Journal of Global Optimization
An efficient and safe framework for solving optimization problems
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Using constraint techniques for a safe and fast implementation of optimality-based reduction
Proceedings of the 2007 ACM symposium on Applied computing
A Sound Floating-Point Polyhedra Abstract Domain
APLAS '08 Proceedings of the 6th Asian Symposium on Programming Languages and Systems
Fast construction of constant bound functions for sparse polynomials
Journal of Global Optimization
Fast and Accurate Bounds on Linear Programs
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
Enhancing numerical constraint propagation using multiple inclusion representations
Annals of Mathematics and Artificial Intelligence
A linear relaxation technique for the position analysis of multiloop linkages
IEEE Transactions on Robotics
MEC-IDC: joint load balancing and power control for distributed Internet Data Centers
Proceedings of the 1st ACM/IEEE International Conference on Cyber-Physical Systems
INFOCOM'10 Proceedings of the 29th conference on Information communications
Automatic abstraction for intervals using Boolean formulae
SAS'10 Proceedings of the 17th international conference on Static analysis
SIAM Journal on Control and Optimization
Transfer function synthesis without quantifier elimination
ESOP'11/ETAPS'11 Proceedings of the 20th European conference on Programming languages and systems: part of the joint European conferences on theory and practice of software
An exact rational mixed-integer programming solver
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Integration of an LP solver into interval constraint propagation
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Synthesis of quantized feedback control software for discrete time linear hybrid systems
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Efficient pruning technique based on linear relaxations
COCOS'03 Proceedings of the Second international conference on Global Optimization and Constraint Satisfaction
A comparison of methods for the computation of affine lower bound functions for polynomials
COCOS'03 Proceedings of the Second international conference on Global Optimization and Constraint Satisfaction
A dynamic program analysis to find floating-point accuracy problems
Proceedings of the 33rd ACM SIGPLAN conference on Programming Language Design and Implementation
Exact solutions to linear programming problems
Operations Research Letters
ICN-RE: redundancy elimination for information-centric networking
Proceedings of the second edition of the ICN workshop on Information-centric networking
Boosting local consistency algorithms over floating-point numbers
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Valid Linear Programming Bounds for Exact Mixed-Integer Programming
INFORMS Journal on Computing
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Model-based synthesis of control software from system-level formal specifications
ACM Transactions on Software Engineering and Methodology (TOSEM)
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Current mixed-integer linear programming solvers are based on linear programming routines that use floating-point arithmetic. Occasionally, this leads to wrong solutions, even for problems where all coefficients and all solution components are small integers. An example is given where many state-of-the-art MILP solvers fail. It is then shown how, using directed rounding and interval arithmetic, cheap pre- and postprocessing of the linear programs arising in a branch-and-cut framework can guarantee that no solution is lost, at least for mixed-integer programs in which all variables can be bounded rigorously by bounds of reasonable size.