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On sparsity of approximate solutions to max-plus linear systems

Pingke Li (2024)

Kybernetika

When a system of one-sided max-plus linear equations is inconsistent, the approximate solutions within an admissible error bound may be desired instead, particularly with some sparsity property. It is demonstrated in this paper that obtaining the sparsest approximate solution within a given L ∞ error bound may be transformed in polynomial time into the set covering problem, which is known to be NP-hard. Besides, the problem of obtaining the sparsest approximate solution within a given L 1 error bound...

On stable least squares solution to the system of linear inequalities

Evald Übi (2007)

Open Mathematics

The system of inequalities is transformed to the least squares problem on the positive ortant. This problem is solved using orthogonal transformations which are memorized as products. Author’s previous paper presented a method where at each step all the coefficients of the system were transformed. This paper describes a method applicable also to large matrices. Like in revised simplex method, in this method an auxiliary matrix is used for the computations. The algorithm is suitable for unstable...

On superlinear multiplier update methods for partial augmented Lagrangian techniques.

Eugenio Mijangos (2002)

Qüestiió

The minimization of a nonlinear function with linear and nonlinear constraints and simple bounds can be performed by minimizing an augmented Lagrangian function, including only the nonlinear constraints. This procedure is particularly interesting in case that the linear constraints are flow conservation equations, as there exist efficient techniques to solve nonlinear network problems. It is then necessary to estimate their multipliers, and variable reduction techniques can be used to carry out...

On the application of insertion techniques for job shop problems with setup times

Yuri N. Sotskov, Thomas Tautenhahn, Frank Werner (2010)

RAIRO - Operations Research

Constructive heuristics for shop scheduling problems are often based on priority (or dispatching) rules. However, recent work has demonstrated that insertion algorithms that step by step insert operations or jobs into partial schedules usually clearly outperform priority rules. In this paper, we consider various job shop scheduling problems with setup times. For each job a specific technological route and a release date are given. Moreover, the jobs are partitioned into groups. A sequence independent...

On the Argmin-sets of stochastic processes and their distributional convergence in Fell-type-topologies

Dietmar Ferger (2011)

Kybernetika

Let ϵ - ( Z ) be the collection of all ϵ -optimal solutions for a stochastic process Z with locally bounded trajectories defined on a topological space. For sequences ( Z n ) of such stochastic processes and ( ϵ n ) of nonnegative random variables we give sufficient conditions for the (closed) random sets ϵ n - ( Z n ) to converge in distribution with respect to the Fell-topology and to the coarser Missing-topology.

On the best choice of a damping sequence in iterative optimization methods.

Leonid N. Vaserstein (1988)

Publicacions Matemàtiques

Some iterative methods of mathematical programming use a damping sequence {αt} such that 0 ≤ αt ≤ 1 for all t, αt → 0 as t → ∞, and Σ αt = ∞. For example, αt = 1/(t+1) in Brown's method for solving matrix games. In this paper, for a model class of iterative methods, the convergence rate for any damping sequence {αt} depending only on time t is computed. The computation is used to find the best damping sequence.

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