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| 2. |
- Garcia, Ricardo, et al.
(author)
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Network design applications of the class of column generation/simplicial decomposition algorithms in convex differentiable optimization
- 2001
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In: Investigacion Operacional. ; 22:2, s. 91-99
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Journal article (peer-reviewed)abstract
- A new class of column generation/simplicial decomposition method for nonlinear convex and differentiable programming is presented. The new algorithm class builds on the intuitively appealing idea that nonlinear column generation problems may be advantageous computationally. Different applications of this methodology are presented, with special attention to the unicommodity and multicommodity network flow problems, which are obtained when some decomposition methods are applied to network design problems.
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| 3. |
- Larsson, Torbjörn, 1957-, et al.
(author)
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A column generation procedure for the side constrained traffic equilibrium problem
- 2004
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In: Transportation Research Part B. - : Elsevier. - 0191-2615 .- 1879-2367. ; 38:1, s. 17-38
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Journal article (peer-reviewed)abstract
- We present a column generation procedure for the side constrained traffic equilibrium problem. A dual stabilization scheme is introduced to improve the computational performance. Computational experiments for the case of linear side constraints are presented. The test problems are well known traffic equilibrium instances where side constraints of link flow capacity type and general linear side constraints are added. The computational results are promising especially for instances with a relatively small number of side constraints.
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| 4. |
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| 5. |
- Larsson, Torbjörn, 1957-, et al.
(author)
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Inverse nonlinear multicommodity flow optimization by column generation
- 2003
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In: Optimization Methods and Software. - : Informa UK Limited. - 1055-6788 .- 1029-4937. ; 18:5, s. 601-613
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Journal article (peer-reviewed)abstract
- We present a solution algorithm for an inverse nonlinear multicommodity network flow problem. This problem is to find link cost adjustments that make a given target link flow solution optimal in a nonlinear multicommodity network flow problem, and that are optimal with respect to a specified objective. The solution procedure uses column generation. We present computational results for instances where the nonlinear multicommodity network flow problems are small and medium scale traffic equilibrium problems, and where system optimal link flows are targeted. The computational results show that the solution procedure is a viable approach for solving medium-scale instances of the inverse traffic equilibrium problem.
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| 6. |
- Larsson, Torbjörn, 1957-, et al.
(author)
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On the convergence of conditional e-subgradient methods for convex programs and convex-concave saddle-point problems
- 2003
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In: European Journal of Operational Research. - 0377-2217 .- 1872-6860. ; 151:3, s. 461-473
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Journal article (peer-reviewed)abstract
- The paper provides two contributions. First, we present new convergence results for conditional e-subgradient algorithms for general convex programs. The results obtained here extend the classical ones by Polyak [Sov. Math. Doklady 8 (1967) 593, USSR Comput. Math. Math. Phys. 9 (1969) 14, Introduction to Optimization, Optimization Software, New York, 1987] as well as the recent ones in [Math. Program. 62 (1993) 261, Eur. J. Oper. Res. 88 (1996) 382, Math. Program. 81 (1998) 23] to a broader framework. Secondly, we establish the application of this technique to solve non-strictly convex-concave saddle point problems, such as primal-dual formulations of linear programs. Contrary to several previous solution algorithms for such problems, a saddle-point is generated by a very simple scheme in which one component is constructed by means of a conditional e-subgradient algorithm, while the other is constructed by means of a weighted average of the (inexact) subproblem solutions generated within the subgradient method. The convergence result extends those of [Minimization Methods for Non-Differentiable Functions, Springer-Verlag, Berlin, 1985, Oper. Res. Lett. 19 (1996) 105, Math. Program. 86 (1999) 283] for Lagrangian saddle-point problems in linear and convex programming, and of [Int. J. Numer. Meth. Eng. 40 (1997) 1295] for a linear-quadratic saddle-point problem arising in topology optimization in contact mechanics.
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- Patriksson, Michael, 1964, et al.
(author)
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On stochastic structural topology optimization
- 2002
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In: Nonsmooth/Nonconvex Mechanics: With Applications in Engineering, Proceedings of the International Conference in memory of Professor P. D. Panagiotopoulos, 5-6 July 2002, Thessaloniki, Greece. ; , s. 97-104
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Conference paper (peer-reviewed)
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- Patriksson, Michael, 1964, et al.
(author)
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Variational geometry and equilibrium
- 2003
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In: Equilibrium Problems and Variational Models. - 9781402074707 ; , s. 347-368
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Conference paper (peer-reviewed)
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