Quadratic programming is in NP
Information Processing Letters
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
WCRE '01 Proceedings of the Eighth Working Conference on Reverse Engineering (WCRE'01)
SDPARA: semiDefinite programming algorithm paRAllel version
Parallel Computing
Large-scale semidefinite programs in electronic structure calculation
Mathematical Programming: Series A and B
Implementation of a primal—dual method for SDP on a shared memory parallel architecture
Computational Optimization and Applications
Precise Interval Analysis vs. Parity Games
FM '08 Proceedings of the 15th international symposium on Formal Methods
Static analysis by policy iteration on relational domains
ESOP'07 Proceedings of the 16th European conference on Programming
Precise fixpoint computation through strategy iteration
ESOP'07 Proceedings of the 16th European conference on Programming
Computing relaxed abstract semantics w.r.t. quadratic zones precisely
SAS'10 Proceedings of the 17th international conference on Static analysis
Solving systems of rational equations through strategy iteration
ACM Transactions on Programming Languages and Systems (TOPLAS)
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Efficient strongly relational polyhedral analysis
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
A policy iteration algorithm for computing fixed points in static analysis of programs
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
Precise relational invariants through strategy iteration
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Abstract acceleration of general linear loops
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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Numerical static program analyses by abstract interpretation, e.g., the problem of inferring bounds for the values of numerical program variables, are faced with the problem that the abstract domains often contain infinite ascending chains. In order to enforce termination within the abstract interpretation framework, a widening/narrowing approach can be applied that trades the guarantee of termination against a potential loss of precision. Alternatively, recently strategy improvement algorithms have been proposed for computing numerical invariants which do not suffer the imprecision incurred by widenings. Before, strategy improvement algorithms have successfully been applied for solving two-players zero-sum games. In this article we discuss and compare max-strategy and min-strategy improvement algorithms for static program analysis. For that, the algorithms are cast within a common general framework of solving systems of fixpoint equations x-=e where the right-hand sides e are maxima of finitely many monotone and concave functions. Then we indicate how the general setting can be instantiated for inferring numerical invariants of programs based on non-linear templates.