New computer methods for global optimization
New computer methods for global optimization
Preconditioners for the interval Gauss-Seidel method
SIAM Journal on Numerical Analysis
Algorithm 681: INTBIS, a portable interval Newton/bisection package
ACM Transactions on Mathematical Software (TOMS)
A collection of test problems for constrained global optimization algorithms
A collection of test problems for constrained global optimization algorithms
Interval Newton/generalized bisection when there are singularities near roots
Annals of Operations Research
Programmer's guide to Fortran 90
Programmer's guide to Fortran 90
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Recent advances in global optimization
Recent advances in global optimization
An efficient method for the numerical evaluation of partial derivatives of arbitrary order
ACM Transactions on Mathematical Software (TOMS)
Algorithm 737: INTLIB—a portable Fortran 77 interval standard-function library
ACM Transactions on Mathematical Software (TOMS)
Software for Interval Arithmetic: A Reasonably Portable Package
ACM Transactions on Mathematical Software (TOMS)
A simple automatic derivative evaluation program
Communications of the ACM
Expression parsing and rigorous computation of bounds on all solutions to practical nonlinear systems
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Algorithm 737: INTLIB—a portable Fortran 77 interval standard-function library
ACM Transactions on Mathematical Software (TOMS)
Algorithm 763: INTERVAL_ARITHMETIC: a Fortran 90 module for an interval data type
ACM Transactions on Mathematical Software (TOMS)
Multisection in Interval Branch-and-Bound Methods for Global Optimization II. Numerical Tests
Journal of Global Optimization
Existence verification for singular and nonsmooth zeros of real nonlinear systems
Mathematics of Computation
A new global optimization method for univariate constrained twice-differentiable NLP problems
Journal of Global Optimization
Interval function and its linear least-squares approximation
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
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An environment for general research into and prototyping of algorithms for reliable constrained and unconstrained global nonlinear optimization and reliable enclosure of all roots of nonlinear systems of equations, with or without inequality constraints, is being developed. This environment should be portable, easy to learn, use, and maintain, and sufficiently fast for some production work. The motivation, design principles, uses, and capabilities for this environment are outlined. The environment includes an interval data type, a symbolic form of automatic differentiation to obtain an internal representation for functions, a special technique to allow conditional branches with operator overloading and interval computations, and generic routines to give interval and noninterval function and derivative information. Some of these generic routines use a special version of the backward mode of automatic differentiation. The package also includes dynamic data structures for exhaustive search algorithms.