Enhanced alternating energy minimization methods for stochastic galerkin matrix equations

2022 ◽  
Author(s):  
Kookjin Lee ◽  
Howard C. Elman ◽  
Catherine E. Powell ◽  
Dongeun Lee
Keyword(s):  
Energy Minimization ◽  
Matrix Equations ◽  
Minimization Methods ◽  
Stochastic Galerkin

Constrained optimization and protein structure determination

1991 ◽  
Vol 261 (2) ◽  
pp. C376-C386 ◽  
Author(s):  
J. Eisenfeld ◽  
S. Vajda ◽  
I. Sugar ◽  
C. DeLisi
Keyword(s):  
Constrained Optimization ◽  
Energy Minimization ◽  
Structure Prediction ◽  
Protein Structure Determination ◽  
Experimental Information ◽  
Local Geometry ◽  
Sequence Information ◽  
Energy Functions ◽  
Minimization Methods ◽  
And Mathematics

Energy minimization is one of the main approaches to the computational determination of macromolecular structure. Due to the approximations in the empirical free-energy functions and due to the computational difficulties in locating their global minima, the problem is at present intractable when the only information available is the sequence of subunits forming the molecule. A less-demanding problem in terms of both physics and mathematics is constrained optimization, which uses additional but incomplete experimental information such as distances between certain atoms. This paper reviews methods for generating molecular structure using bond lengths and angles as variables and shows how the structure can be fully specified in terms of local geometry. The analysis permits precise statements to be made about the minimum set of distances that specify a unique structure without recourse to energy minimization. We then discuss the complementary situation, i.e., structure prediction with energy minimization based only on sequence information. Finally, we show how distance constraints can be incorporated into energy minimization methods.

scholarly journals A Comparative Study of Energy Minimization Methods for Markov Random Fields with Smoothness-Based Priors

2008 ◽  
Vol 30 (6) ◽  
pp. 1068-1080 ◽  
Author(s):  
R. Szeliski ◽  
R. Zabih ◽  
D. Scharstein ◽  
O. Veksler ◽  
V. Kolmogorov ◽  
...  
Keyword(s):  
Comparative Study ◽  
Random Fields ◽  
Energy Minimization ◽  
Markov Random Fields ◽  
Markov Random ◽  
Minimization Methods

Schottky-Energy Calculation: Relation between Force-Balance and Energy-Minimization Procedures

1972 ◽  
Vol 50 (8) ◽  
pp. 729-735 ◽  
Author(s):  
J. H. Simpson
Keyword(s):  
Energy Minimization ◽  
Force Balance ◽  
Energy Calculation ◽  
Energy Calculations ◽  
Minimization Methods

An attempt is made to determine whether the variations between results of Schottky-energy calculations in the literature arise chiefly from the parameters used or from the method of attacking the problem. Results of the force-balance and energy-minimization methods of calculating the displacements of the ions surrounding the defect and the dipoles upon them are compared. It is concluded that the differences are small and explicable provided the same set of crystal parameters is used. The reasons for some of the discrepancies in the literature are discussed.

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