Project Scheduling

Nowadays, construction projects grow in complexity and size. So, finding feasible schedules which efficiently use scarce resources is a challenging task within project management. Project scheduling consists of determining the starting and finishing times of the activities in a project. These activities are linked by precedence relations and their processing requires one or more resources. … Read more

Adaptive First-Order Methods for General Sparse Inverse Covariance Selection

In this paper, we consider estimating sparse inverse covariance of a Gaussian graphical model whose conditional independence is assumed to be partially known. Similarly as in [5], we formulate it as an $l_1$-norm penalized maximum likelihood estimation problem. Further, we propose an algorithm framework, and develop two first-order methods, that is, adaptive spectral projected gradient … Read more

Generalized power method for sparse principal component analysis

In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant principal component of a data matrix, or more components at once, respectively. While the initial formulations involve nonconvex functions, … Read more

Core Routing on Dynamic Time-Dependent Road Networks

Route planning in large scale time-dependent road networks is an important practical application of the shortest paths problem that greatly benefits from speedup techniques. In this paper we extend a two-levels hierarchical approach for point-to-point shortest paths computations to the time-dependent case. This method, also known as core routing in the literature for static graphs, … Read more

Sensitivity analysis of the optimal solutions to Huff-type competitive location and design problems

A chain wants to set up a single new facility in a planar market where similar facilities of competitors, and possibly of its own chain, are already present. Fixed demand points split their demand probabilistically over all facilities in the market proportionally with their attraction to each facility, determined by the different perceived qualities of … Read more

Bidirectional A* Search on Time-Dependent Road Networks

The computation of point-to-point shortest paths on time-dependent road networks has a large practical interest, but very few works propose efficient algorithms for this problem. We propose a novel approach which tackles one of the main complications of route planning in time-dependent graphs, which is the difficulty of using bidirectional search: since the exact arrival … Read more

Reformulations and Algorithms for the Optimization of Switching Decisions in Nonlinear Optimal Control

In model-based nonlinear optimal control switching decisions that can be optimized often play an important role. Prominent examples of such hybrid systems are gear switches for transport vehicles or valves in chemical engineering. Optimization algorithms need to take the discrete nature of the variables that model these switching decisions into account. Unnecessarily, for many applications … Read more

Optimal Scenario Tree Reduction for Stochastic Streamflows in Power Generation Planning Problems

The mid-term operation planning of hydro-thermal power systems needs a large number of synthetic sequences to represent accurately stochastic streamflows. These sequences are generated by a periodic autoregressive model. If the number of synthetic sequences is too big, the optimization planning problem may be too difficult to solve. To select a small set of sequences … Read more

Fixed point and Bregman iterative methods for matrix rank minimization

The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The linearly constrained nuclear norm minimization is a convex relaxation of this problem. Although it can be cast as a semidefinite programming problem, the nuclear norm minimization problem is expensive to solve when the … Read more

Global Optimization for the Design of Space Trajectories

The problem of optimally designing a trajectory for a space mission is considered in this paper. Actual mission design is a complex, multi-disciplinary and multi-objective activity with relevant economic implications. In this paper we will consider some simplified models proposed by the European Space Agency as test problems for global optimization. We show that many … Read more