Bilinear Programming
نویسنده
چکیده
f(x, y) = a x + x Qy + b y, where a, x ∈ R, b, y ∈ R, and Q is a matrix of dimension n ×m. It is easy to see that bilinear functions compose a subclass of quadratic functions. We refer to optimization problems with bilinear objective and/or constraints as bilinear problems, and they can be viewed as a subclass of quadratic programming. Bilinear programming has various applications in constrained bimatrix games, Markovian assignment and complementarity problems. Many 0-1 integer programs can be formulated as bilinear problems. An extensive discussion of different applications can be found in [3]. Concave piecewise linear and fixed charge network flow problems, which are very common in the supply chain management, can be also solved using bilinear formulations (see, e.g., [5] and [6]).
منابع مشابه
Generation of disjointly constrained bilinear programming test problems
This paper describes a technique for generating disjointly constrained bilinear programming test problems with known solutions and properties. The proposed construction technique applies a simple random tranformation of variables to a separable bilinear programming problem that is constructed by combining disjoint low-dimensional bilinear programs.
متن کاملAn integer linear programming approach for bilinear integer programming
We introduce a new Integer Linear Programming (ILP) approach for solving Integer Programming (IP) problems with bilinear objectives and linear constraints. The approach relies on a series of ILP approximations of the bilinear IP. We compare this approach with standard linearization techniques on random instances and a set of real-world product bundling problems.
متن کاملAn integer linear programming approach for a class of bilinear integer programs
We propose an Integer Linear Programming (ILP) approach for solving integer programming problems with bilinear objectives and linear constraints. Our approach is based on nding upper and lower bounds for the optimal bilinear objective function, and using the upper bound to produce a tight binary decomposition of an ensemble in the bilinear objective function. This allows us to transform the ori...
متن کاملRobust Approximate Bilinear Programming Robust Approximate Bilinear Programming for Value Function Approximation
Existing value function approximation methods have been successfully used in many applications, but they often lack useful a priori error bounds. We propose a new approximate bilinear programming formulation of value function approximation, which employs global optimization. The formulation provides strong a priori guarantees on both robust and expected policy loss by minimizing specific norms ...
متن کاملPrimal-dual bilinear programming solution of the absolute value equation
We propose a finitely terminating primal-dual bilinear programming algorithm for the solution of the NP-hard absolute value equation (AVE): Ax− |x| = b, where A is an n× n square matrix. The algorithm, which makes no assumptions on AVE other than solvability, consists of a finite number of linear programs terminating at a solution of the AVE or at a stationary point of the bilinear program. The...
متن کامل