In this study, we introduce a distribution network design problem that determines the locations and capacities of the relief distribution points in the last mile network, while considering demand- and network-related uncertainties in the post-disaster environment. The problem addresses the critical concerns of relief organizations in designing last mile networks, which are providing accessible and … Read more
The steepest descent algorithm with exact line searches (Cauchy algorithm) is inefficient, generating oscillating step lengths and a sequence of points converging to the span of the eigenvectors associated with the extreme eigenvalues. The performance becomes very good if a short step is taken at every (say) 10 iterations. We show a new method for … Read more
In this paper after algebraical and geometrical preliminaries we present a Gram-Schmidt-type algorithmical conjecture, which if true settles the long-standing Hadamard conjecture concerning the existence of orthogonal matrices with elements of the same absolute value. CitationUnpublished, ELTE Operation Research Report 2015/1ArticleDownload View PDF
We develop algorithmic innovations for the dual decomposition method to address two-stage stochastic programs with mixed-integer recourse and provide a parallel software implementation that we call DSP. Our innovations include the derivation of valid inequalities that tighten Lagrangian subproblems and that allow the guaranteed recovery of feasible solutions for problems without (relative) complete recourse. We … Read more
The pooling problem is a nonconvex nonlinear programming problem with numerous applications. The nonlinearities of the problem arise from bilinear constraints that capture the blending of raw materials. Bilinear constraints are well-studied and significant progress has been made in solving large instances of the pooling problem to global optimality. This is due in no small … Read more
We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited by the interior-point method, allowing the (either … Read more
We describe simple and exact duals, and certificates of infeasibility and weak infeasibility in conic linear programming which do not rely on any constraint qualification, and retain most of the simplicity of the Lagrange dual. In particular, some of our infeasibility certificates generalize the row echelon form of a linear system of equations, and the … Read more
The alternating direction of multipliers (ADMM) is a form of augmented Lagrangian algorithm that has experienced a renaissance in recent years due to its applicability to optimization problems arising from “big data” and image processing applications, and the relative ease with which it may be implemented in parallel and distributed computational environments. While it is … Read more
In this paper we study genericity for the following parameterized class of nonlinear programs: \begin{eqnarray*} \textrm{minimize } f_u(x) := f(x) – \langle u, x \rangle \quad \textrm{subject to } \quad x \in S, \end{eqnarray*} where $f \colon \mathbb{R}^n \rightarrow \mathbb{R}$ is a polynomial function and $S \subset \mathbb{R}^n$ is a closed semialgebraic set, which is … Read more
In this paper we consider the class of polynomial optimization problems with inequality and equality constraints, in which every problem of the class is obtained by perturbations of the objective function, while the constraint functions are kept fixed. Under certain assumptions, we establish some stability properties (e.g., strong H\”older stability with explicitly determined exponents, semicontinuity, … Read more