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11
A Computational Study of the Homogeneous Algorithm for LargeScale Convex Optimization
, 1997
"... Recently the authors have proposed a homogeneous and selfdual algorithm for solving the monotone complementarity problem (MCP) [5]. The algorithm is a single phase interiorpoint type method, nevertheless it yields either an approximate optimal solution or detects a possible infeasibility of th ..."
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Cited by 13 (1 self)
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Recently the authors have proposed a homogeneous and selfdual algorithm for solving the monotone complementarity problem (MCP) [5]. The algorithm is a single phase interiorpoint type method, nevertheless it yields either an approximate optimal solution or detects a possible infeasibility of the problem. In this paper we specialize the algorithm to the solution of general smooth convex optimization problems that also possess nonlinear inequality constraints and free variables. We discuss an implementation of the algorithm for largescale sparse convex optimization. Moreover, we present computational results for solving quadratically constrained quadratic programming and geometric programming problems, where some of the problems contain more than 100,000 constraints and variables. The results indicate that the proposed algorithm is also practically efficient. Department of Management, Odense University, Campusvej 55, DK5230 Odense M, Denmark. Email: eda@busieco.ou.dk y ...
A nonlinear Knapsack Problem
 Operations Research Letters
, 1995
"... The nonlinear Knapsack problem is to maximize a separable concave objective function, subject to a single "packing" constraint, in nonnegative variables. We consider this problem in integer and continuous variables, and also when the packing constraint is convex. Although the nonlinear Knapsack prob ..."
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Cited by 10 (0 self)
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The nonlinear Knapsack problem is to maximize a separable concave objective function, subject to a single "packing" constraint, in nonnegative variables. We consider this problem in integer and continuous variables, and also when the packing constraint is convex. Although the nonlinear Knapsack problem appears difficult in comparison with the linear Knapsack problem, we prove that its complexity is similar. We demonstrate for the nonlinear Knapsack problem in n integer variables and knapsack volume limit B, a fully polynomial approximation scheme with running time ()((1/e 2) (n + l/e2)) (omitting polylog terms); and for the continuous case an algorithm delivering an eaccurate solution in O(nlog(B/~)) operations.
A survey on the continuous nonlinear resource allocation problem
 Eur. J. Oper. Res
, 2008
"... 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 a ..."
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Cited by 6 (1 self)
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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
Interior Point Methods for SecondOrder Cone Programming and OR Applications
, 2003
"... Interior point methods (IPM) have been developed for all types of constrained optimization problems. In this work the extension of IPM to second order cone programming (SOCP) is studied based on the work of Andersen, Roos, and Terlaky. SOCP minimizes a linear objective function over the direct produ ..."
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Cited by 3 (0 self)
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Interior point methods (IPM) have been developed for all types of constrained optimization problems. In this work the extension of IPM to second order cone programming (SOCP) is studied based on the work of Andersen, Roos, and Terlaky. SOCP minimizes a linear objective function over the direct product of quadratic cones, rotated quadratic cones, and an a#ne set. It is described in detail how to convert several application problems to SOCP. Moreover, a proof is given of the existence of the step for the infeasible longstep pathfollowing method. Furthermore, variants are developed of both longstep pathfollowing and of predictorcorrector algorithms. Numerical results are presented and analyzed for those variants using test cases obtained from a number of application problems. 1
Marginal Bidding: An Application of the Equimarginal Principle to Bidding in TAC SCM
"... Abstract. We present a fast and effective bidding strategy for the Trading Agent Competition in Supply Chain Management (TAC SCM). In TAC SCM, manufacturers compete to procure computer parts from suppliers (the procurement problem), and then sell assembled computers to customers in reverse auctions ..."
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Cited by 2 (1 self)
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Abstract. We present a fast and effective bidding strategy for the Trading Agent Competition in Supply Chain Management (TAC SCM). In TAC SCM, manufacturers compete to procure computer parts from suppliers (the procurement problem), and then sell assembled computers to customers in reverse auctions (the bidding problem). This paper is concerned only with bidding, in which an agent must decide how many computers to sell and at what prices to sell them. We propose a greedy solution, Marginal Bidding, inspired by the Equimarginal Principle, which states that revenue is maximized among possible uses of a resource when the return on the last unit of the resource is the same across all areas of use. We show experimentally that certain variations of Marginal Bidding can compute bids faster than our ILP solution, which enables Marginal Bidders to consider future demand as well as current demand, and hence achieve greater revenues when knowledge of the future is valuable. 1
A Partial Ranking Algorithm for Resource Allocation Problems
, 2001
"... We present an algorithm to solve resource allocation problems with a single resource, a convex separable objective function, a convex separable resourceusage constraint and bounded variables. Through evaluation of speci...c functions in the lower and/or upper bounds, we obtain information on whethe ..."
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Cited by 1 (0 self)
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We present an algorithm to solve resource allocation problems with a single resource, a convex separable objective function, a convex separable resourceusage constraint and bounded variables. Through evaluation of speci...c functions in the lower and/or upper bounds, we obtain information on whether or not these bounds are binding. Once this information is available for all variables, the optimum is found through determination of the unique root of a strictly decreasing function. A comparison is made with the currently known most ecient algorithms. Keywords: Programming, nonlinear: resource allocation. Programming, algorithms: partial ranking. Corresponding author: CentER for Economic Research and Department of Econometrics and Operations Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands. Tel: ++3113 4662913. Fax: ++31134663280. Email: a.m.b.DeWaegenaere@kub.nl. y CentER for Economic Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands. 1 1
A GRÖBNER BASES METHODOLOGY FOR SOLVING MULTIOBJECTIVE POLYNOMIAL INTEGER PROGRAMS
, 902
"... Abstract. Multiobjective discrete programming is a wellknown family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the last years. However, the polynomial case has not been deeply studied due to its theoretical and computation ..."
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Abstract. Multiobjective discrete programming is a wellknown family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the last years. However, the polynomial case has not been deeply studied due to its theoretical and computational difficulties. This paper presents an algebraic approach for solving these problems. We propose a methodology based on transforming the polynomial optimization problem in the problem of solving one or more systems of polynomial equations and we use certain Gröbner bases to solve these systems. Different transformations give different methodologies that are analyzed and compared from a theoretical point of view and by some computational experiments via the algorithms that they induce. 1.
Node generation and capacity . . . networks
, 2013
"... This article investigates methods for reallocation of service capacities in open Jackson networks in order to minimize either a system’s mean total workinprocess or its response time. The focus is mainly on a method called node generation, by which capacity can be transferred from a node in echelo ..."
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This article investigates methods for reallocation of service capacities in open Jackson networks in order to minimize either a system’s mean total workinprocess or its response time. The focus is mainly on a method called node generation, by which capacity can be transferred from a node in echelon j to a newly generated node in echelon j + 1. The proposed procedure is compared with the more conventional capacity redistribution method, by which capacity can be transferred from any node in echelon j to existing successor nodes in echelon j + 1. Formulation of each method as a mathematical programming problem reveals the structure of the optimal solution for both problems. The motivation for considering these approaches stems from reallife settings, in particular, from a production line or supply chains where the two types of capacity reallocation are applied. Heuristic methods are developed to solve relatively large networks in tractable time. Numerical results and analyses are presented.
unknown title
"... Parallel machine matchup scheduling with manufacturing cost considerations ..."
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Parallel machine matchup scheduling with manufacturing cost considerations