Rigorous Global Search: Continuous Problems

By R. B. Kearfott. 1996

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Citations in the corpus

Formal Security Analysis of Neural Networks using Symbolic Intervals (2018, background): “Then we resort to Smear Function [21, 22]: Si(X) = max1≤ j≤d |Ji j|w(X j), where the input X j with the largest smear value is the most effective interval input for the targeted output Yi.”
A novel approach in uncertain programming part I: new arithmetic and order relation for interval numbers (2006, methodology): “Interval analysis methods have been applied to Analytical Hierarchy Process (AHP) [12, 35, 41], fuzzy AHP [4], systems and optimization theory [22, 23, 24, 25, 32, 37, 44], fuzzy”
Reliable nonlinear parameter estimation using interval analysis: error-in-variable approach (2000, background): “Several good introductions to interval analysis are available (e.g., Kearfott, 1996).”
Validated solutions of initial value problems for parametric ODEs (2007, background): “Several good introductions to interval analysis, as well as interval arithmetic and other aspects of computing with intervals, are available [8, 6, 9, 31].”
Complete search in continuous global optimization and constraint satisfaction (2004, methodology): “(ii) GlobSol: Global Solver (in Fortran 90) Kearfott (1996b, 2003) www.mscs.mu.edu/∼globsol/ Branch and bound code for global optimization with general factorable constraints, with rigorously guaranteed results (even round-off is accounted for correctly).”
Reliable Phase Stability Analysis for Excess Gibbs Energy Models (2000, background): “This technique provides the power to find, with confidence,nclosuresof all solutions of a system of nonlinear equations (e.g., Neumaier, 1990; Kearfott, 1996), and to find with total reliability the global minimum of a nonlinear objective function (e.g., Hansen, 1992; Kearfott, 1996), provided only…”
From Bandits to Monte-Carlo Tree Search: The Optimistic Principle Applied to Optimization and Planning (2014, methodology): “A large body of algorithmic work has been developed using branch-and-bound techniques [94, 67, 79, 71, 98, 57, 110] such as Lipschitz optimization where the function is assumed to be globally Lipschitz.”
Planar Location and Design of a New Facility with Inner and Outer Competition: An Interval Lexicographical-like Solution Procedure (2007, background): “where the symbol ∗ stands for +, −, · and / ,a nd wherex/ y is only defined if 0 ∈ y. Definition (5) is equivalent to simple constructive rules (see Hansen, 1992; Kearfott, 1996; Ratschek and Rokne, 1988).”
New interval methodologies for reliable chemical process modeling (2002, methodology): “However, as discussed and illustrated by Hansen (1992) and Kearfott (1996), this set is in general not an interval, and may have a very complex polygonal geometry.”
Standardized notation in interval analysis (2010, background): “We hope that the suggested notation will appear persuasive to authors in interval analysis and its applications, convincing them that using it is likely to improve the communication of ideas in interval analysis to colleagues and potential users.”