Minimization over the l1-ball using an active-set non-monotone projected gradient

The l1-ball is a nicely structured feasible set that is widely used in many fields (e.g., machine learning, statistics and signal analysis) to enforce some sparsity in the model solutions. In this paper, we devise an active-set strategy for efficiently dealing with minimization problems over the l1-ball and embed it into a tailored algorithmic scheme … Read more

Global Optimization for Nonconvex Programs via Convex Proximal Point Method

The nonconvex program plays an important role in the field of optimization and has a lot of applications in practice. However, for general nonconvex programming problems, the lack of verifiable global optimal conditions and the multiple local minimizers make global optimization hard in computation. In this paper, a convex proximal point algorithm (CPPA) is considered … Read more

Optimal deployment of indoor wireless local area networks

We present a two-phase methodology to address the problem of optimally deploying indoor wireless local area networks. In the first phase, we use Helmholtz’s equation to simulate electromagnetic fields in a typical environment such as an office floor. The linear system which results from the discretization of this partial differential equation is solved with a … Read more

A novel decomposition approach for holistic airline optimization

Airlines face many different planning processes until the day of operation. These include Fleet Assignment, Tail Assignment and the associated control of ground processes between consecutive flights, called Turnaround Handling. All of these planning problems have in common that they often need to be reoptimized on the day of execution due to unplanned events. In … Read more

Locating Platforms and Scheduling a Fleet of Drones for Emergency Delivery of Perishable Items

Motivated by issues dealing with delivery of emergency medical products during humanitarian disasters, this paper addresses the general problem of delivering perishable items to remote demands accessible only by helicopters or drones. Each drone operates out of platforms that may be moved when not in use and each drone has a limited delivery range to … Read more

On the exactness of the eps-constraint method for bi-objective integer nonlinear programming

The eps-constraint method is a well-known scalarization technique used for multiobjective optimization. We explore how to properly define the step size parameter of the method in order to guarantee its exactness when dealing with problems having two nonlinear objective functions and integrality constraints on the variables. Under specific assumptions, we prove that the number of … Read more

Full-low evaluation methods for derivative-free optimization

We propose a new class of rigorous methods for derivative-free optimization with the aim of delivering efficient and robust numerical performance for functions of all types, from smooth to non-smooth, and under different noise regimes. To this end, we have developed Full-Low Evaluation methods, organized around two main types of iterations. The first iteration type … Read more

A New Multipoint Symmetric Secant Method with a Dense Initial Matrix

In large-scale optimization, when either forming or storing Hessian matrices are prohibitively expensive, quasi-Newton methods are often used in lieu of Newton’s method because they only require first-order information to approximate the true Hessian.  Multipoint symmetric secant (MSS) methods can be thought of as generalizations of quasi-Newton methods in that they attempt to impose additional requirements on their approximation of the … Read more

Global optimization using random embeddings

We propose a random-subspace algorithmic framework for global optimization of Lipschitz-continuous objectives, and analyse its convergence using novel tools from conic integral geometry. X-REGO randomly projects, in a sequential or simultaneous manner, the high- dimensional original problem into low-dimensional subproblems that can then be solved with any global, or even local, optimization solver. We estimate … Read more

A spectral PALM algorithm for matrix and tensor-train based Dictionary Learning

Dictionary Learning (DL) is one of the leading sparsity promoting techniques in the context of image classification, where the “dictionary” matrix D of images and the sparse matrix X are determined so as to represent a redundant image dataset. The resulting constrained optimization problem is nonconvex and non-smooth, providing several computational challenges for its solution. … Read more