Ergodic Results in Subgradient Optimization

1996 ◽  
pp. 229-248 ◽  
Author(s):  
Torbjörn Larsson ◽  
Michael Patriksson ◽  
Ann-Brith Strömberg
Keyword(s):  
Subgradient Optimization

scholarly journals Improved Small Molecule Identification through Learning Combinations of Kernel Regression Models

Metabolites ◽  
2019 ◽  
Vol 9 (8) ◽  
pp. 160 ◽  
Author(s):  
Céline Brouard ◽  
Antoine Bassé ◽  
Florence d’Alché-Buc ◽  
Juho Rousu
Keyword(s):  
Small Molecule ◽  
Kernel Regression ◽  
Feature Space ◽  
Molecular Structures ◽  
Subgradient Optimization ◽  
Hinge Loss ◽  
Fast Training ◽  
Negative Ionization Mode ◽  
Ionization Mode ◽  
Negative Ionization

In small molecule identification from tandem mass (MS/MS) spectra, input–output kernel regression (IOKR) currently provides the state-of-the-art combination of fast training and prediction and high identification rates. The IOKR approach can be simply understood as predicting a fingerprint vector from the MS/MS spectrum of the unknown molecule, and solving a pre-image problem to find the molecule with the most similar fingerprint. In this paper, we bring forward the following improvements to the IOKR framework: firstly, we formulate the IOKRreverse model that can be understood as mapping molecular structures into the MS/MS feature space and solving a pre-image problem to find the molecule whose predicted spectrum is the closest to the input MS/MS spectrum. Secondly, we introduce an approach to combine several IOKR and IOKRreverse models computed from different input and output kernels, called IOKRfusion. The method is based on minimizing structured Hinge loss of the combined model using a mini-batch stochastic subgradient optimization. Our experiments show a consistent improvement of top-k accuracy both in positive and negative ionization mode data.

Distributed multi-step subgradient optimization for multi-agent system

2019 ◽  
Vol 128 ◽  
pp. 26-33 ◽  
Author(s):  
Chaoyong Li ◽  
Sai Chen ◽  
Jianqing Li ◽  
Feng Wang
Keyword(s):  
Multi Agent System ◽  
Subgradient Optimization ◽  
Agent System ◽  
Multi Agent

Cutting Plane Methods for Analytical Target Cascading With Augmented Lagrangian Coordination

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Wenshan Wang ◽  
Vincent Y. Blouin ◽  
Melissa K. Gardenghi ◽  
Georges M. Fadel ◽  
Margaret M. Wiecek ◽  
...  
Keyword(s):  
Large Scale ◽  
Augmented Lagrangian ◽  
Optimization Problems ◽  
Cutting Plane ◽  
Analytical Target Cascading ◽  
Cutting Plane Methods ◽  
Subgradient Optimization ◽  
Decomposition Approach ◽  
Target Cascading ◽  
Augmented Lagrangian Coordination

Analytical target cascading (ATC), a hierarchical, multilevel, multidisciplinary coordination method, has proven to be an effective decomposition approach for large-scale engineering optimization problems. In recent years, augmented Lagrangian relaxation methods have received renewed interest as dual update methods for solving ATC decomposed problems. These problems can be solved using the subgradient optimization algorithm, the application of which includes three schemes for updating dual variables. To address the convergence efficiency disadvantages of the existing dual update schemes, this paper investigates two new schemes, the linear and the proximal cutting plane methods, which are implemented in conjunction with augmented Lagrangian coordination for ATC-decomposed problems. Three nonconvex nonlinear example problems are used to show that these two cutting plane methods can significantly reduce the number of iterations and the number of function evaluations when compared to the traditional subgradient update methods. In addition, these methods are also compared to the method of multipliers and its variants, showing similar performance.

scholarly journals An Improved Subgradiend Optimization Technique for Solving IPs with Lagrangean Relaxation

2013 ◽  
Vol 61 (2) ◽  
pp. 135-140
Author(s):  
M Babul Hasan ◽  
Md Toha
Keyword(s):  
Dual Problem ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Concave Function ◽  
Optimization Method ◽  
Duality Gap ◽  
Dual Function ◽  
Subgradient Optimization ◽  
Step Size ◽  
Primal Problem

The objective of this paper is to improve the subgradient optimization method which is used to solve non-differentiable optimization problems in the Lagrangian dual problem. One of the main drawbacks of the subgradient method is the tuning process to determine the sequence of step-lengths to update successive iterates. In this paper, we propose a modified subgradient optimization method with various step size rules to compute a tuning- free subgradient step-length that is geometrically motivated and algebraically deduced. It is well known that the dual function is a concave function over its domain (regardless of the structure of the cost and constraints of the primal problem), but not necessarily differentiable. We solve the dual problem whenever it is easier to solve than the primal problem with no duality gap. However, even if there is a duality gap the solution of the dual problem provides a lower bound to the primal optimum that can be useful in combinatorial optimization. Numerical examples are illustrated to demonstrate the method. DOI: http://dx.doi.org/10.3329/dujs.v61i2.17059 Dhaka Univ. J. Sci. 61(2): 135-140, 2013 (July)

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