scholarly journals Copositive Programming by Simplicial Partition

Informatica ◽  
2011 ◽  
Vol 22 (4) ◽  
pp. 601-614 ◽  
Author(s):  
Julius Žilinskas
Keyword(s):  
Copositive Programming ◽  
Simplicial Partition

A hybrid of the simplicial partition-based Bayesian global search with the local descent

2020 ◽  
Vol 24 (23) ◽  
pp. 17601-17608 ◽  
Author(s):  
Antanas Žilinskas ◽  
Linas Litvinas
Keyword(s):  
Global Search ◽  
Simplicial Partition

scholarly journals Immobile Indices and CQ-Free Optimality Criteria for Linear Copositive Programming Problems

2020 ◽  
Vol 28 (1) ◽  
pp. 89-107
Author(s):  
O. I. Kostyukova ◽  
T. V. Tchemisova ◽  
O. S. Dudina
Keyword(s):  
Optimality Criteria ◽  
Copositive Programming

Analysis of Positive Systems Using Copositive Programming

2020 ◽  
Vol 4 (2) ◽  
pp. 444-449
Author(s):  
Teruki Kato ◽  
Yoshio Ebihara ◽  
Tomomichi Hagiwara
Keyword(s):  
Positive Systems ◽  
Copositive Programming

scholarly journals Induced Matchings and the v-Number of Graded Ideals

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2860
Author(s):  
Gonzalo Grisalde ◽  
Enrique Reyes ◽  
Rafael H. Villarreal
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Matching Number ◽  
Edge Ideal ◽  
Induced Matching ◽  
Simplicial Partition ◽  
The Family ◽  
Induced Matchings ◽  
Edge Ring ◽  
Insight Into

We give a formula for the v-number of a graded ideal that can be used to compute this number. Then, we show that for the edge ideal I(G) of a graph G, the induced matching number of G is an upper bound for the v-number of I(G) when G is very well-covered, or G has a simplicial partition, or G is well-covered connected and contains neither four, nor five cycles. In all these cases, the v-number of I(G) is a lower bound for the regularity of the edge ring of G. We classify when the induced matching number of G is an upper bound for the v-number of I(G) when G is a cycle and classify when all vertices of a graph are shedding vertices to gain insight into the family of W2-graphs.

scholarly journals On new methods to construct lower bounds in simplicial branch and bound based on interval arithmetic

2021 ◽  
Author(s):  
B. G.-Tóth ◽  
L. G. Casado ◽  
E. M. T. Hendrix ◽  
F. Messine
Keyword(s):  
Global Optimization ◽  
Lower Bounds ◽  
Branch And Bound ◽  
Interval Arithmetic ◽  
Efficient Global Optimization ◽  
Test Problems ◽  
Simplicial Partition ◽  
Monotonicity Test ◽  
Low Dimensional ◽  
Linear Relaxations

AbstractBranch and Bound (B&B) algorithms in Global Optimization are used to perform an exhaustive search over the feasible area. One choice is to use simplicial partition sets. Obtaining sharp and cheap bounds of the objective function over a simplex is very important in the construction of efficient Global Optimization B&B algorithms. Although enclosing a simplex in a box implies an overestimation, boxes are more natural when dealing with individual coordinate bounds, and bounding ranges with Interval Arithmetic (IA) is computationally cheap. This paper introduces several linear relaxations using gradient information and Affine Arithmetic and experimentally studies their efficiency compared to traditional lower bounds obtained by natural and centered IA forms and their adaption to simplices. A Global Optimization B&B algorithm with monotonicity test over a simplex is used to compare their efficiency over a set of low dimensional test problems with instances that either have a box constrained search region or where the feasible set is a simplex. Numerical results show that it is possible to obtain tight lower bounds over simplicial subsets.

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