A general class of branch-and-bound methods in global optimization with some new approaches for concave minimization

1986 ◽  
Vol 51 (2) ◽  
pp. 271-291 ◽  
Author(s):  
R. Horst
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
General Class ◽  
Concave Minimization ◽  
New Approaches ◽  
Branch And Bound Methods

scholarly journals BRANCH AND BOUND WITH SIMPLICIAL PARTITIONS FOR GLOBAL OPTIMIZATION

2008 ◽  
Vol 13 (1) ◽  
pp. 145-159 ◽  
Author(s):  
J. Žilinskas
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Linear Inequality ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Combinatorial Approach ◽  
Rectangular Shape ◽  
Linear Inequality Constraints ◽  
Advantages And Disadvantages ◽  
Branch And Bound Methods

Branch and bound methods for global optimization are considered in this paper. Advantages and disadvantages of simplicial partitions for branch and bound are shown. A new general combinatorial approach for vertex triangulation of hyper‐rectangular feasible regions is presented. Simplicial partitions may be used to vertex triangulate feasible regions of non rectangular shape defined by linear inequality constraints. Linear inequality constraints may be used to avoid symmetries in optimization problems.

scholarly journals On derivative based bounding for simplicial branch and bound

2021 ◽  
Author(s):  
Eligius M.T. Hendrix ◽  
Boglarka G. -Tóth ◽  
Frederic Messine ◽  
Leocadio G. Casado
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Branch And Bound ◽  
Partial Derivative ◽  
Interval Arithmetic ◽  
Objective Function Value ◽  
Search Space ◽  
Second Derivative ◽  
Branch And Bound Methods

Simplicial based Global Optimization branch and bound methods require tight bounds on the objective function value. Recently, a renewed interest appears on bound calculation based on Interval Arithmetic by Karhbet and Kearfott (2017) and on exploiting second derivative bounds by Mohand (2021). The investigated question here is how partial derivative ranges can be used to provide bounds of the objective function value over the simplex. Moreover, we provide theoretical properties of how this information can be used from a monotonicity perspective to reduce the search space in simplicial branch and bound.

scholarly journals A Global Optimization Algorithm for Sum of Linear Ratios Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yuelin Gao ◽  
Siqiao Jin
Keyword(s):  
Global Optimization ◽  
Lower Bound ◽  
Programming Problem ◽  
Branch And Bound ◽  
Numerical Experiments ◽  
Original Problem ◽  
Bilinear Programming ◽  
Global Optimization Algorithm ◽  
Product Function ◽  
Optimal Value

We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.

Sign in / Sign up

Export Citation Format

Share Document