Journal ArticleDOI
A global optimization method, αBB, for general twice-differentiable constrained NLPs—II. Implementation and computational results
TLDR
The performance of the proposed algorithm and its alternative underestimators is studied through their application to a variety of problems and a number of rules for branching variable selection and variable bound updates are shown to enhance convergence rates.About:
This article is published in Computers & Chemical Engineering.The article was published on 1998-08-20. It has received 324 citations till now. The article focuses on the topics: Global optimization & Nonlinear programming.read more
Citations
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Journal ArticleDOI
Branching and bounds tighteningtechniques for non-convex MINLP
TL;DR: An sBB software package named couenne (Convex Over- and Under-ENvelopes for Non-linear Estimation) is developed and used for extensive tests on several combinations of BT and branching techniques on a set of publicly available and real-world MINLP instances and is compared with a state-of-the-art MINLP solver.
Journal ArticleDOI
Mixed-integer nonlinear optimization
TL;DR: An emerging area of mixed-integer optimal control that adds systems of ordinary differential equations to MINLP is described and a range of approaches for tackling this challenging class of problems are discussed, including piecewise linear approximations, generic strategies for obtaining convex relaxations for non-convex functions, spatial branch-and-bound methods, and a small sample of techniques that exploit particular types of non- Convex structures to obtain improved convex Relaxations.
Journal ArticleDOI
A sequential parametric convex approximation method with applications to nonconvex truss topology design problems
TL;DR: It is shown that the approximate convex problem solved at each inner iteration can be cast as a conic quadratic programming problem, hence large scale TTD problems can be efficiently solved by the proposed method.
Journal ArticleDOI
A global optimization method, αBB, for general twice-differentiable constrained NLPs — I. Theoretical advances
TL;DR: The deterministic global optimization algorithm, αBB (α-based Branch and Bound) is presented, which offers mathematical guarantees for convergence to a point arbitrarily close to the global minimum for the large class of twice-differentiable NLPs.
Journal ArticleDOI
Non-convex mixed-integer nonlinear programming: A survey
Samuel Burer,Adam N. Letchford +1 more
TL;DR: In this paper, the authors survey the literature on non-convex mixed-integer nonlinear programs, discussing applications, algorithms, and software, and special attention is paid to the case in which the objective and constraint functions are quadratic.
References
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Journal ArticleDOI
CHARMM: A program for macromolecular energy, minimization, and dynamics calculations
Bernard R. Brooks,Robert E. Bruccoleri,Barry D. Olafson,David J. States,S. Swaminathan,Martin Karplus +5 more
TL;DR: The CHARMM (Chemistry at Harvard Macromolecular Mechanics) as discussed by the authors is a computer program that uses empirical energy functions to model macromolescular systems, and it can read or model build structures, energy minimize them by first- or second-derivative techniques, perform a normal mode or molecular dynamics simulation, and analyze the structural, equilibrium, and dynamic properties determined in these calculations.
Journal ArticleDOI
An all atom force field for simulations of proteins and nucleic acids.
TL;DR: An all atom potential energy function for the simulation of proteins and nucleic acids and the first general vibrational analysis of all five nucleic acid bases with a molecular mechanics potential approach is presented.
Journal ArticleDOI
Energy parameters in polypeptides. 10. Improved geometrical parameters and nonbonded interactions for use in the ECEPP/3 algorithm, with application to proline-containing peptides
George Nemethy,Kenneth D. Gibson,Kathleen A. Palmer,Chang No. Yoon,Germana Paterlini,Adriana Zagari,Shirley Rumsey,Harold A. Scheraga +7 more
TL;DR: In this paper, the ECEPP parameters used in the computer program to describe the geometry of amino acid residues and the potential energy of interactions have been updated based on recently available experimental information.
Book
Automatic Differentiation: Techniques and Applications
TL;DR: This paper presents a procedure for automatic computation of gradients, Jacobians, Hessians, and applications to optimization in the form of a discrete-time model.
Journal ArticleDOI
A global optimization method, αBB, for general twice-differentiable constrained NLPs — I. Theoretical advances
TL;DR: The deterministic global optimization algorithm, αBB (α-based Branch and Bound) is presented, which offers mathematical guarantees for convergence to a point arbitrarily close to the global minimum for the large class of twice-differentiable NLPs.