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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 ..."
Abstract

Cited by 22 (2 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 ...
Joint lot sizing and tool management in a CNC environment
 Computers in Industry 40
, 1999
"... We propose a new algorithm to solve lot sizing, tool allocation and machining conditions optimization problems simultaneously to minimize total production cost in a CNC environment. Most of the existing lot sizing and tool management methods solve these problems independently using a twolevel optim ..."
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Cited by 1 (1 self)
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We propose a new algorithm to solve lot sizing, tool allocation and machining conditions optimization problems simultaneously to minimize total production cost in a CNC environment. Most of the existing lot sizing and tool management methods solve these problems independently using a twolevel optimization approach. Thus, we not only improve the overall solution by exploiting the interactions among these decision making problems, but also prevent any infeasibility that might occur for the tool management problem due to decisions made at the lot sizing level. The computational experiments showed that in a set of randomly generated problems 22.5 % of solutions found by the twolevel approach were infeasible and the proposed joint approach improved the solution on the average by 6.79 % for the remaining
A computational study of the homogeneous algorithm for largescale convex optimization
, 1996
"... Key words: Monotone complementarity problem, homogeneous and selfdual model, interiorpoint algorithms, largescale convex optimization. 1 Introduction In 1984 Karmarkar [31] presented an interiorpoint method for linear programming (LP) and since then interiorpoint algorithms enjoyed great public ..."
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Key words: Monotone complementarity problem, homogeneous and selfdual model, interiorpoint algorithms, largescale convex optimization. 1 Introduction In 1984 Karmarkar [31] presented an interiorpoint method for linear programming (LP) and since then interiorpoint algorithms enjoyed great publicity for two reasons. First, these algorithms solve LP problems in polynomial time, as proved by Karmarkar and many others. Secondly, interiorpoint algorithms have demonstrated excellent practical performance when solving largescale LP problems, see Lustig et al. [37]. It was soon realized (see Gill et al. [25]) that Karmarkar's method was closely related to the logarithmic barrier algorithm for general nonlinear programming studied by Fiacco and McCormick [23] and others in the sixties. Hence, it is natural to investigate the efficiency of the interiorpoint methods for solving more general classes of problems. In general good complexity results could only be expected for solving convex optimization problems.