Simple Bound Constraints Optimization

2017 ◽  
pp. 147-184
Author(s):  
Neculai Andrei
Keyword(s):  
Bound Constraints

Bound constraints handling in Differential Evolution: An experimental study

2019 ◽  
Vol 50 ◽  
pp. 100453 ◽  
Author(s):  
Rafał Biedrzycki ◽  
Jarosław Arabas ◽  
Dariusz Jagodziński
Keyword(s):  
Experimental Study ◽  
Differential Evolution ◽  
Bound Constraints ◽  
Constraints Handling

Reverse maximum flow problem under the weighted Chebyshev distance

2018 ◽  
Vol 52 (4-5) ◽  
pp. 1107-1121 ◽  
Author(s):  
Javad Tayyebi ◽  
Abumoslem Mohammadi ◽  
Seyyed Mohammad Reza Kazemi
Keyword(s):  
Flow Problem ◽  
Maximum Flow ◽  
Binary Search ◽  
Second Phase ◽  
Sink Node ◽  
Search Technique ◽  
Bound Constraints ◽  
Maximum Flow Problem ◽  
Optimal Value ◽  
Two Phases

Given a network G(V, A, u) with two specific nodes, a source node s and a sink node t, the reverse maximum flow problem is to increase the capacity of some arcs (i, j) as little as possible under bound constraints on the modifications so that the maximum flow value from s to t in the modified network is lower bounded by a prescribed value v0. In this paper, we study the reverse maximum flow problem when the capacity modifications are measured by the weighted Chebyshev distance. We present an efficient algorithm to solve the problem in two phases. The first phase applies the binary search technique to find an interval containing the optimal value. The second phase uses the discrete type Newton method to obtain exactly the optimal value. Finally, some computational experiments are conducted to observe the performance of the proposed algorithm.

scholarly journals Disjoint interval bound constraints using the alternating direction method of multipliers (ADMM) for geologically constrained inversion: Application to gravity data

Geophysics ◽  
2020 ◽  
pp. 1-45
Author(s):  
Vitaliy Ogarko ◽  
Jérémie Giraud ◽  
Roland Martin ◽  
Mark Jessell
Keyword(s):  
Gravity Data ◽  
Alternating Direction Method ◽  
Rock Properties ◽  
Model Parameters ◽  
Method Of Multipliers ◽  
Geological Modeling ◽  
Bound Constraints ◽  
Data Inversion ◽  
Alternating Direction ◽  
Geological Information

To reduce uncertainties in reconstructed images, geological information must be introduced in a numerically robust and stable way during the geophysical data inversion procedure. In the context of potential (gravity) data inversion, it is important to bound the physical properties by providing probabilistic information on the number of lithologies and ranges of values of possibly existing related rock properties (densities). For this purpose, we introduce a generalization of bounding constraints for geophysical inversion based on the alternating direction method of multipliers (ADMM). The flexibility of the proposed technique enables us to take into account petrophysical information as well as probabilistic geological modeling, when it is available. The algorithm introduces a priori knowledge in terms of physically acceptable bounds of model parameters based on the nature of the modeled lithofacies in the region under study. Instead of introducing only one interval of geologically acceptable values for each parameter representing a set of rock properties, we define sets of disjoint intervals using the available geological information. Different sets of intervals are tested, such as quasi-discrete (or narrow) intervals as well as wider intervals provided by geological information obtained from probabilistic geological modeling. Narrower intervals can be used as soft constraints encouraging quasi-discrete inversions. The algorithm is first applied to a synthetic 2D case for proof-of-concept validation and then to the 3D inversion of gravity data collected in the Yerrida basin (Western Australia). Numerical convergence tests show the robustness and stability of the bound constraints we apply, which is not always trivial for constrained inversions. This technique can be a more reliable uncertainty reduction method as well as an alternative to other petrophysically or geologically constrained inversions based on more classical “clustering” or Gaussian-mixture approaches.

scholarly journals On the binary classification problem in discriminant analysis using linear programming methods

2020 ◽  
Vol 30 (1) ◽  
Author(s):  
Michael O. Olusola ◽  
Sydney I. Onyeagu
Keyword(s):  
Linear Programming ◽  
Discriminant Analysis ◽  
Binary Classification ◽  
Classification Problem ◽  
Solution Technique ◽  
Phase Method ◽  
Bound Constraints ◽  
Two Phase ◽  
Linear Discriminant ◽  
Binary Classification Problem

This paper is centred on a binary classification problem in which it is desired to assign a new object with multivariate features to one of two distinct populations as based on historical sets of samples from two populations. A linear discriminant analysis framework has been proposed, called the minimised sum of deviations by proportion (MSDP) to model the binary classification problem. In the MSDP formulation, the sum of the proportion of exterior deviations is minimised subject to the group separation constraints, the normalisation constraint, the upper bound constraints on proportions of exterior deviations and the sign unrestriction vis-à-vis the non-negativity constraints. The two-phase method in linear programming is adopted as a solution technique to generate the discriminant function. The decision rule on group-membership prediction is constructed using the apparent error rate. The performance of the MSDP has been compared with some existing linear discriminant models using a previously published dataset on road casualties. The MSDP model was more promising and well suited for the imbalanced dataset on road casualties.

Sign in / Sign up

Export Citation Format

Share Document