/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Introduction to linear and nonlinear programming

Remaining useful life estimation - A review on the statistical data driven approaches

A survey of maintenance policies of deteriorating systems

/pdf/sequencing-and-scheduling-algorithms-and-complexity-lnutyrr3kz.pdf

Sequencing and scheduling: algorithms and complexity

For the general quadratic assignment problem as well as for a planar version of this problem, we extend earlier work by Burkard and Fincke to prove that the ratio of the maximal to the minimal solution value converges to 1 almost surely. In fact, any solution value can almost surely be written asymptotically as a simple, explicitly given function of the problem size. Theoretical analysis and computational experiments reveal the convergence to be relatively fast.

Asymptotic Properties of the Quadratic Assignment Problem

A number of optimization methods require as a first step the construction of a dominating set (a set containing an optimal solution) enjoying properties such as compactness or convexity. In this paper, we address the problem of constructing dominating sets for problems whose objective is a componentwise nondecreasing function of (possibly an infinite number of) convex functions, and we show how to obtain a convex dominating set in terms of dominating sets of simpler problems. The applicability of the results obtained is illustrated with the statement of new localization results in the fields of linear regression and location.

/pdf/dominating-sets-for-convex-functions-with-some-applications-1au29leufw.pdf

Dominating sets for convex functions with some applications

We define two simple algorithms for the bin covering problem and give their asymptotic performance.

/pdf/two-simple-algorithms-for-bin-covering-2634m43m6n.pdf

Two simple algorithms for bin covering

https://repub.eur.nl/pub/11700/Two-dimensional_rectangle_packing.pdf

Two-dimensional rectangle packing: on-line methods and results

In this paper we explore the relations between the standard dual problem of a convex generalized fractional programming problem and the “partial” dual problem proposed by Barros et al. (1994). Taking into account the similarities between these dual problems and using basic duality results we propose a new algorithm to directly solve the standard dual of a convex generalized fractional programming problem, and hence the original primal problem, if strong duality holds. This new algorithm works in a similar way as the algorithm proposed in Barros et al. (1994) to solve the “partial” dual problem. Although the convergence rates of both algorithms are similar, the new algorithm requires slightly more restrictive assumptions to ensure a superlinear convergence rate. An important characteristic of the new algorithm is that it extends to the nonlinear case the Dinkelbach-type algorithm of Crouzeix et al. (1985) applied to the standard dual problem of a generalized linear fractional program. Moreover, the general duality results derived for the nonlinear case, yield an alternative way to derive the standard dual of a generalized linear fractional program. The numerical results, in case of quadratic-linear ratios and linear constraints, show that solving the standard dual via the new algorithm is in most cases more efficient than applying directly the Dinkelbach-type algorithm to the original generalized fractional programming problem. However, the numerical results also indicate that solving the alternative dual (Barros et al., 1994) is in general more efficient than solving the standard dual.

J. B. G. Frenk

Papers

Asymptotic Properties of the Quadratic Assignment Problem

Dominating sets for convex functions with some applications

Two simple algorithms for bin covering

Two-dimensional rectangle packing: on-line methods and results

Using duality to solve generalized fractional programming problems