Experimental design is a classical statistics problem and its aim is to estimate an unknown m-dimensional vector from linear measurements where a Gaussian noise is introduced in each measurement. For the combinatorial experimental design problem, the goal is to pick k out of the given n experiments so as to make the most accurate estimate … Read more
This document presents a, chronologically ordered, bibliography of scientific publications on the superiorization methodology and perturbation resilience of algorithms which is compiled and continuously updated by us at: http://math.haifa.ac.il/yair/bib-superiorization-censor.html. Since the topic is relatively new it is possible to trace the work that has been published about it since its inception. To the best of … Read more
We investigate new convex relaxations for the pooling problem, a classic nonconvex production planning problem in which input materials are mixed in intermediate pools, with the outputs of these pools further mixed to make output products meeting given attribute percentage requirements. Our relaxations are derived by considering a set which arises from the formulation by … Read more
In this paper, we propose a generalized Benders decomposition-based branch and bound algorithm, GBDBAB, to solve two-stage convex 0-1 mixed-integer nonlinear stochastic programs with mixed-integer variables in both first and second stage decisions. In order to construct the convex hull of the MINLP subproblem for each scenario in closed-form, we first represent each MINLP subproblem … Read more
We consider minimization of a smooth nonconvex objective function using an iterative algorithm based on Newton’s method and linear conjugate gradient, with explicit detection and use of negative curvature directions for the Hessian of the objective function. The algorithm tracks Newton-conjugate gradient procedures developed in the 1980s closely, but includes enhancements that allow worst-case complexity … Read more
As an alternative to traditional integer programming (IP), decision diagrams (DDs) provide a new solution technology for discrete problems based on their combinatorial structure and dynamic programming representation. While the literature mainly focuses on the competitive aspects of DDs as a stand-alone solver, we investigate their complementary role by studying IP techniques that can be … Read more
Two critical yet frequently conflicting objectives for logistics and transportation service companies are improving customer satisfaction and reducing transportation cost. In particular, given a net- work of customer requests with preferred service times, it is very challenging to find vehicle routes and service schedules simultaneously that respect all operating constraints and minimize the total transportation … Read more
This paper considers again the well-known problem of dealing with non-convex regions during the minimization of a nonlinear function F(x) by Newton-like methods. The proposal made here involves a curvilinear search along an approximation to the continuous steepest descent path defined by the solution of the ODE dx/dt = -grad F(x). The algorithm we develop … Read more
We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the numerical conditioning of the LP relaxations resulting from the branching and cutting operations can be effectively predicted and whether … Read more
Previous work showed that total variation superiorization (TVS) improves reconstructed image quality in proton computed tomography (pCT). The structure of the TVS algorithm has evolved since then and this work investigated if this new algorithmic structure provides additional benefits to pCT image quality. Structural and parametric changes introduced to the original TVS algorithm included: (1) … Read more