Supporting Global Numerical Optimization of Rational Functions by Generic Symbolic Convexity Tests

DOI10.1007/978-3-642-15274-0_19zbMath1290.65053OpenAlexW1495020149MaRDI QIDQ3589077

Thomas Sturm, Stefan Vigerske, Winfried Neun

Publication date: 10 September 2010

Published in: Computer Algebra in Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-15274-0_19

zbMATH Keywords

convex functionsimplementationreal quantifier eliminationReducenonlinear global optimizationhybrid symbolic-numeric computation

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Numerical optimization and variational techniques (65K10)

Related Items

SUSPECT: MINLP special structure detector for Pyomo, ANTIGONE: algorithms for coNTinuous/Integer global optimization of nonlinear equations

Uses Software

• QEPCAD
• REDUCE
• REDLOG
• MINLPLib
• Excel
• COPS
• FrontLine

Cites Work

• Unnamed Item
• Unnamed Item
• Investigating algebraic and logical algorithms to solve Hopf bifurcation problems in algebraic biology
• Quantifier elimination for real algebra -- the quadratic case and beyond
• The complexity of linear problems in fields
• Real quantifier elimination is doubly exponential
• Partial cylindrical algebraic decomposition for quantifier elimination
• Rigorous convex underestimators for general twice-differentiable problems
• Convexification and global optimization in continuous and mixed-integer nonlinear programming. Theory, algorithms, software, and applications
• Global optimization in engineering design
• MINLPLib—A Collection of Test Models for Mixed-Integer Nonlinear Programming
• Algorithms and Software for Convex Mixed Integer Nonlinear Programs
• Convexity and Concavity Detection in Computational Graphs: Tree Walks for Convexity Assessment
• Efficient Calculation of Bounds on Spectra of Hessian Matrices
• Investigating Generic Methods to Solve Hopf Bifurcation Problems in Algebraic Biology
• Optimization of the Design and Partial-Load Operation of Power Plants Using Mixed-Integer Nonlinear Programming
• Numerical Optimization
• On the combinatorial and algebraic complexity of quantifier elimination