A survey on the continuous nonlinear resource allocation problem

• Published in: European journal of operational research Vol. 185; no. 1; pp. 1 - 46
• Main Author: Patriksson, Michael
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 2008; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Algorithms; Applied sciences; Convex programming; Exact sciences and technology; Inventory; Inventory control, production control. Distribution; Lagrange multiplier; Large scale optimization; Logistics; Nonlinear programming; Operational research and scientific management; Operational research. Management science; Operations research; Optimization; Resource allocation; Studies; Large scale optimization; Nonlinear programming; Convex programming; Inventory; Logistics; Operations research; Statistical analysis; Balancing; Probabilistic approach; Resource allocation; Algorithmics; Non linear programming; Equilibrium condition; History; Economic sciences; Modeling; Optimization; Production management; Lagrange multiplier; Convex function; Large scale; Military
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2006.12.006

Our problem of interest consists of minimizing a separable, convex and differentiable function over a convex set, defined by bounds on the variables and an explicit constraint described by a separable convex function. Applications are abundant, and vary from equilibrium problems in the engineering and economic sciences, through resource allocation and balancing problems in manufacturing, statistics, military operations research and production and financial economics, to subproblems in algorithms for a variety of more complex optimization models. This paper surveys the history and applications of the problem, as well as algorithmic approaches to its solution. The most common techniques are based on finding the optimal value of the Lagrange multiplier for the explicit constraint, most often through the use of a type of line search procedure. We analyze the most relevant references, especially regarding their originality and numerical findings, summarizing with remarks on possible extensions and future research.