# Bilinear problems

• Christodoulos A. Floudas
• Pãnos M. Pardalos
• William R. Esposito
• Zeynep H. Gümüş
• Stephen T. Harding
• John L. Klepeis
• Clifford A. Meyer
• Carl A. Schweiger
Chapter
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 33)

## Abstract

Bilinear problems are an important subclass of nonconvex quadratic programming problems whose applications encompass pooling and blending, separation sequencing, heat exchanger network design and multicommodity network flow problems. The general form of a bilinear problem is given by
$$\begin{gathered} \mathop {\min }\limits_{x,y} \quad {x^T}\,{A_0}y + c_0^Tx + d_0^Ty \hfill \\ s.t.\quad {x^T}{A_i}y + c_i^Tx + d_i^Ty \leqslant {b_i},\;i = 1, \ldots ,p \hfill \\ \quad \quad {x^T}{A_i}y + c_i^Tx + d_i^T = {b_i},\;i = p + 1, \ldots ,p + a \hfill \\ \quad \quad x \in {R^n} \hfill \\ \quad \quad y \in {R^m} \hfill \\ \end{gathered}$$
where x and y are n- and m-dimensional vectors respectively, A i , i = 1, . . . , p + q, are n × m matrices, c i , i = 1, ... , p + q, are n-dimensional real vectors, i = 0, ... , p + q, are m-dimensional real vectors and b is a (p+q)-dimensional real vector.

## Keywords

Objective Function Global Solution Distillation Column Feed Stream Convex Inequality
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Authors and Affiliations

• Christodoulos A. Floudas
• 1
• Pãnos M. Pardalos
• 2
• 1
• William R. Esposito
• 1
• Zeynep H. Gümüş
• 1
• Stephen T. Harding
• 1
• John L. Klepeis
• 1
• Clifford A. Meyer
• 1
• Carl A. Schweiger
• 1
1. 1.Department of Chemical EngineeringPrinceton UniversityPrincetonUSA
2. 2.Department of Industrial and Systems EngineeringUniversity of FloridaUSA