## A survey on the continuous nonlinear resource allocation problem (2008)

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Venue: | Eur. J. Oper. Res |

Citations: | 7 - 1 self |

### BibTeX

@ARTICLE{Patriksson08asurvey,

author = {Michael Patriksson},

title = {A survey on the continuous nonlinear resource allocation problem},

journal = {Eur. J. Oper. Res},

year = {2008},

pages = {1--46}

}

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### Abstract

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. 1 Introduction and

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Citation Context ...(Methodology) Bisection search (Citations) Applications: promotion models ([McC7X]); capital budgeting ([Lau70, MSM83, DMS88]); hydrological studies, clique problems in graphs, and location problems (=-=[GHS80]-=-); for the continuous case: resource allocation ([BiH79, LuG75]); algorithms for multicommodity flows ([HWC74]) and stochastic programs with network recourse ([NiZ93]); additional references found in ... |

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Citation Context ...2 j − rjxj, qj ≥ 0; linear equality (aj = 1, b = 1); lj = 0, uj = ∞ (Origin) Subproblem for each origin–destination pair in the traffic assignment problem within the scaled reduced gradient method of =-=[LaP92]-=- (Methodology) A Newton method, wherein q ′′ , at breakpoints where it is not defined, is replaced by the left (right) derivative of q ′ when q ′ is negative (positive) (Citations) Refers to [HKL80, B... |