On the solution of special generalized upper-bounded problems: The LP/GUB knapsack problem and the λ-form separable convex objective function problem

Author(s):  
Saul I. Gass ◽  
Stephen P. Shao
2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Wanping Yang ◽  
Jinkai Zhao ◽  
Fengmin Xu

The constrained rank minimization problem has various applications in many fields including machine learning, control, and signal processing. In this paper, we consider the convex constrained rank minimization problem. By introducing a new variable and penalizing an equality constraint to objective function, we reformulate the convex objective function with a rank constraint as a difference of convex functions based on the closed-form solutions, which can be reformulated as DC programming. A stepwise linear approximative algorithm is provided for solving the reformulated model. The performance of our method is tested by applying it to affine rank minimization problems and max-cut problems. Numerical results demonstrate that the method is effective and of high recoverability and results on max-cut show that the method is feasible, which provides better lower bounds and lower rank solutions compared with improved approximation algorithm using semidefinite programming, and they are close to the results of the latest researches.


2008 ◽  
Vol 47 (22) ◽  
pp. 4061 ◽  
Author(s):  
Jian Liu ◽  
Jiubin Tan ◽  
Chenguang Zhao

2015 ◽  
Vol 68 ◽  
pp. 41-47 ◽  
Author(s):  
Asha Rani ◽  
Gian Luca Foresti ◽  
Christian Micheloni

2020 ◽  
Vol 36 (1) ◽  
pp. 141-146
Author(s):  
SIMEON REICH ◽  
ALEXANDER J. ZASLAVSKI

"Given a Lipschitz and convex objective function of an unconstrained optimization problem, defined on a Banach space, we revisit the class of regular vector fields which was introduced in our previous work on descent methods. We study, in particular, the asymptotic behavior of the sequence of values of the objective function for a certain inexact process generated by a regular vector field when the sequence of computational errors converges to zero and show that this sequence of values converges to the infimum of the given objective function of the unconstrained optimization problem."


2020 ◽  
Author(s):  
Samah Boukhari ◽  
Isma Dahmani ◽  
Mhand Hifi

In this paper, we propose to solve the knapsack problem with setups by combining mixed linear relaxation and local branching. The problem with setups can be seen as a generalization of 0–1 knapsack problem, where items belong to disjoint classes (or families) and can be selected only if the corresponding class is activated. The selection of a class involves setup costs and resource consumptions thus affecting both the objective function and the capacity constraint. The mixed linear relaxation can be viewed as driving problem, where it is solved by using a special blackbox solver while the local branching tries to enhance the solutions provided by adding a series of invalid / valid constraints. The performance of the proposed method is evaluated on benchmark instances of the literature and new large-scale instances. Its provided results are compared to those reached by the Cplex solver and the best methods available in the literature. New results have been reached.


Sign in / Sign up

Export Citation Format

Share Document