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
We propose ARock, an asynchronous parallel algorithmic framework for finding a fixed point to a nonexpansive operator. In the framework, a set of agents (machines, processors, or cores) update a sequence of randomly selected coordinates of the unknown variable in an asynchronous parallel fashion. As special cases of ARock, novel algorithms for linear systems, convex … 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
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
The Probabilistic Traveling Salesman Problem, introduced in 1985 by Jaillet, is one of the fundamental stochastic versions of the Traveling Salesman Problem: After the tour is chosen, each vertex is deleted with given probability 1-p. The eliminated vertices are bypassed which leads to shorter tours. The aim is to minimize the expected tour length. The … Read more