Best network flow bounds for the quadratic knapsack problem
COMO '86 Lectures given at the third session of the Centro Internazionale Matematico Estivo (C.I.M.E.) on Combinatorial optimization
An approximate method for local optima for nonlinear mixed integer programming problems
Computers and Operations Research
Lagrangean methods for 0-1 quadratic problems
Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
Fast equi-partitioning of rectangular domains using stripe decomposition
Discrete Applied Mathematics
Augmented Lagrangian Duality and Nondifferentiable Optimization Methods in Nonconvex Programming
Journal of Global Optimization
Exact Solution of the Quadratic Knapsack Problem
INFORMS Journal on Computing
On augmented Lagrangians for Optimization Problems with a Single Constraint
Journal of Global Optimization
Greedy, genetic, and greedy genetic algorithms for the quadratic knapsack problem
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian*
Journal of Global Optimization
An inexact modified subgradient algorithm for nonconvex optimization
Computational Optimization and Applications
Quadratic resource allocation with generalized upper bounds
Operations Research Letters
Zero duality gap in integer programming: P-norm surrogate constraint method
Operations Research Letters
Optimization and Knowledge-Based Technologies
Informatica
Generalized quadratic multiple knapsack problem and two solution approaches
Computers and Operations Research
Hi-index | 0.00 |
In this study, the performance of the modified subgradient algorithm (MSG) to solve the 0-1 quadratic knapsack problem (QKP) was examined. The MSG was proposed by Gasimov for solving dual problems constructed with respect to sharp Augmented Lagrangian function. The MSG has some important proven properties. For example, it is convergent, and it guarantees zero duality gap for the problems such that its objective and constraint functions are all Lipschtz. Additionally, the MSG has been successfully used for solving non-convex continuous and some combinatorial problems with equality constraints since it was first proposed. In this study, the MSG was used to solve the QKP which has an inequality constraint. The first step in solving the problem was converting zero-one nonlinear QKP problem into continuous nonlinear problem by adding only one constraint and not adding any new variables. Second, in order to solve the continuous QKP, dual problem with "zero duality gap" was constructed by using the sharp Augmented Lagrangian function. Finally, the MSG was used to solve the dual problem, by considering the equality constraint in the computation of the norm. To compare the performance of the MSG with some other methods, some test instances from the relevant literature were solved both by using the MSG and by using three different MINLP solvers of GAMS software. The results obtained were presented and discussed.