A finite test set for an integer maximization problem enables us to verify whether a feasible point attains the global maximum. We establish in this paper several general results that apply to integer maximization problems with nonlinear objective functions. Citation Operations Research Letters 36 (2008) 439–443 Article Download View On Test Sets for Nonlinear Integer … Read more
We study a planning problem arising in SDH/WDM multi-layer telecommunication network design. The goal is to find a minimum cost installation of link and node hardware of both network layers such that traffic demands can be realized via grooming and a survivable routing. We present a mixed-integer programming formulation that takes many practical side constraints … Read more
In this paper, simple linear programming procedure is proposed for generating all efficient extreme points and all efficient extreme rays of a multiple objective linear programming problem (V P). As an application we solve the linear multiplicative programming associated with the problem (VP). Citation submitted Article Download View Generating All Efficient Extreme Points in Multiple … Read more
We present a matrix-free line search algorithm for large-scale equality constrained optimization that allows for inexact step computations. For strictly convex problems, the method reduces to the inexact sequential quadratic programming approach proposed by Byrd et al. [SIAM J. Optim. 19(1) 351–369, 2008]. For nonconvex problems, the methodology developed in this paper allows for the … Read more
Linear support vector machine training can be represented as a large quadratic program. We present an efficient and numerically stable algorithm for this problem using interior point methods, which requires only O(n) operations per iteration. Through exploiting the separability of the Hessian, we provide a unified approach, from an optimization perspective, to 1-norm classification, 2-norm … Read more
We consider the single item lot-sizing problem with capacities that are non-decreasing over time. When the cost function is i) non-speculative or Wagner-Whitin (for instance, constant unit production costs and non-negative unit holding costs), and ii) the production set-up costs are non-increasing over time, it is known that the minimum cost lot-sizing problem is polynomially … Read more
The notion of a secant for locally Lipschitz continuous functions is introduced and a new algorithm to locally minimize nonsmooth, nonconvex functions based on secants is developed. We demonestrate that the secants can be used to design an algorithm to find descent directions of locally Lipschitz continuous functions. This algorithm is applied to design a … Read more
We provide information on the Survivable Network Design Library (SNDlib), a data library for fixed telecommunication network design that can be accessed at http://sndlib.zib.de. In version 1.0, the library contains data related to 22 networks which, combined with a set of selected planning parameters, leads to 830 network planning problem instances. In this paper, we … Read more
Let L_n be the n-dimensional second order cone. A linear map from R^m to R^n is called positive if the image of L_m under this map is contained in L_n. For any pair (n,m) of dimensions, the set of positive maps forms a convex cone. We construct a linear matrix inequality of size (n-1)(m-1) that … Read more
A direct search method for the class of problems considered by Lewis and Torczon [\textit{SIAM J. Optim.}, 12 (2002), pp. 1075-1089] is developed. Instead of using an augmented Lagrangian method, a simplicial approximation method to the feasible set is implicitly employed. This allows the points our algorithm considers to conveniently remain within an \textit{a priori} … Read more