First-Order Necessary Conditions in Optimal Control

Journal of Optimization Theory and Applications - In an earlier analysis of strong variation algorithms for optimal control problems with endpoint inequality constraints, Mayne and Polak provided...     

Visualization of enantiomers in cholesteric solvents through deuterium NMR

Abstract

Proton decoupled deuterium NMR of mixtures of enantiomers in homogeneously oriented cholesteric solvents produces simple spectra with linewidths of 10 to 50 Hz in cases where the proton spectra would give second order patterns so complicated as to defy analysis. The chiral solvent orders each of a pair of enantiomers differently which results in a difference in the residual quadrupolar coupling constant yielding well resolved spectra for each enantiomer. That the technique constitutes a new tool for measurement of enantiomeric ratios is illustrated using several chiral benzylic alcohols.     

Rapid parameterization of small molecules using the force field toolkit

The inability to rapidly generate accurate and robust parameters for novel chemical matter continues to severely limit the application of molecular dynamics simulations to many biological systems of interest, especially in fields such as drug discovery. Although the release of generalized versions of common classical force fields, for example, General Amber Force Field and CHARMM General Force Field, have posited guidelines for parameterization of small molecules, many technical challenges remain that have hampered their wide‐scale extension. The Force Field Toolkit (ffTK), described herein, minimizes common barriers to ligand parameterization through algorithm and method development, automation of tedious and error‐prone tasks, and graphical user interface design. Distributed as a VMD plugin, ffTK facilitates the traversal of a clear and organized workflow resulting in a complete set of CHARMM‐compatible parameters. A variety of tools are provided to generate quantum mechanical target data, setup multidimensional optimization routines, and analyze parameter performance. Parameters developed for a small test set of molecules using ffTK were comparable to existing CGenFF parameters in their ability to reproduce experimentally measured values for pure‐solvent properties (<15% error from experiment) and free energy of solvation (±0.5 kcal/mol from experiment). © 2013 Wiley Periodicals, Inc.     

Efficient domain partitioning algorithms for global optimization of rational and Lipschitz continuous functions

A domain partitioning algorithm for minimizing or maximizing a Lipschitz continuous function is enhanced to yield two new, more efficient algorithms. The use of interval arithmetic in the case of rational functions and the estimates of Lipschitz constants valid in subsets of the domain in the case of others and the addition of local optimization have resulted in an algorithm which, in tests on standard functions, performs well.     

An algorithm for global optimization of Lipschitz continuous functions

An algorithm is presented which locates the global minimum or maximum of a function satisfying a Lipschitz condition. The algorithm uses lower bound functions defined on a partitioned domain to generate a sequence of lower bounds for the global minimum. Convergence is proved, and some numerical results are presented.     

Energy Planning and Policy

Journal of the Operational Research Society -     

An efficient algorithm for solving inequalities

An efficient algorithm for solving a finite system of inequalities in a finite number of iterations is described and analyzed.This work was supported by the UK Science and Engineering Research Council