Combinatorial optimization | Dynamic programming | NP-complete problems | Packing problems | Pseudo-polynomial time algorithms

Quadratic knapsack problem

The quadratic knapsack problem (QKP), first introduced in 19th century, is an extension of knapsack problem that allows for quadratic terms in the objective function: Given a set of items, each with a weight, a value, and an extra profit that can be earned if two items are selected, determine the number of items to include in a collection without exceeding capacity of the knapsack, so as to maximize the overall profit. Usually, quadratic knapsack problems come with a restriction on the number of copies of each kind of item: either 0, or 1. This special type of QKP forms the 0-1 quadratic knapsack problem, which was first discussed by Gallo et al.The 0-1 quadratic knapsack problem is a variation of knapsack problems, combining the features of unbounded knapsack problem, 0-1 knapsack problem and quadratic knapsack problem. (Wikipedia).

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Related pages

Combinatorial optimization | Pseudo-polynomial time | Convex function | Linearization | Decision problem | Diagonally dominant matrix | Dynamic programming | Lagrangian relaxation | Lagrange multiplier | Discrete uniform distribution | Greedy algorithm | Combinatorial auction | Clique problem | Binary data | Knapsack problem | Concave function | List of knapsack problems | Continuous knapsack problem | Optimization problem | Convex set