This paper presents an exact solution method based on a new linearization scheme for the 0-1 Quadratic Knapsack Problem (QKP) which consists of maximizing a quadratic pseudo-Boolean function with non negative coefficients subject to a linear capacity constraint. Contrasting to traditional linearization schemes, our approach only adds one extra variable. We first convert (QKP) into an equivalent...

We present a very general chaining method which allows one to control the supremum of the empirical process suph∈H |N−1 ∑N i=1 h (Xi)− Eh2| in rather general situations. We use this method to establish two main results. First, a quantitative (non asymptotic) version of the classical Bai-Yin Theorem on the singular values of a random matrix with i.i.d entries that have heavy tails, and second, a...

Understanding the method that consumers use to sample through alternatives is paramount to correctly estimating their preference and search cost parameters. Identifying consumers’ search method has been the subject of two recent papers (De los Santos et al. 2012; Honka and Chintagunta, 2014). Both of these papers find that the simultaneous search model more accurately describes consumers’ searc...

In the paper, a fully discrete Multistep characteristic finite volume element method is introduced and analyzed for approximating the solution of a nonlinear-hyperbolic equation in 2-space variables. Piecewise quadratic trial functions and piecewise constant test functions are used to finally obtain error estimate O(∆t + h). A numerical experiment is given which showed the method is practicable.

We present an experimental analysis of neighborhood combinations for local search based metaheuristic algorithms, using the Unconstrained Binary Quadratic Programming (UBQP) problem as a case study. The goal of the analysis is to help understand why, when and how some neighborhoods can be favorably combined to increase their search power. Our study investigates combined neighborhoods with two t...

The problem of low-thrust trajectory optimization in highly perturbed dynamics is a stressing case for many optimization tools. Highly nonlinear dynamics and continuous thrust are each, separately, non-trivial problems in the field of optimal control, and when combined, the problem is even more difficult. This paper describes a fast, robust method to design a trajectory in the CRTBP (circular r...

This paper describes a GRASP with path-relinking heuristic for the quadratic assignment problem. GRASP is a multi-start procedure, where different points in the search space are probed with local search for high-quality solutions. Each iteration of GRASP consists of the construction of a randomized greedy solution, followed by local search, starting from the constructed solution. Path-relinking...

In this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-Archimedean number with $alpha^{-2}neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic $alpha$-functional equation (0.1) in non-Archimedean Banach spaces.