Pablo A. Lotito

A Class of Inexact Variable Metric Proximal Point Algorithms

For the problem of solving maximal monotone inclusions, we present a rather general class of algorithms, which contains hybrid inexact proximal point methods as a special case and allows for the use of a variable metric in subproblems. The global convergence and local linear rate of convergence are established under standard assumptions. We demonstrate the advantage of variable metric implementation in the case of solving systems of smooth monotone equations by the proximal Newton method.

Detecting pedestrians on a Movement Feature Space

This work aims at detecting pedestrians in surveillance video sequences. A pre-processing step detects motion regions on the image using a scene background model based on level lines, which generates a Movement Feature Space, and a family of oriented histogram descriptors. A cascade of boosted classifiers generates pedestrian hypotheses using this feature space. Then, a linear Support Vector Machine validates the hypotheses that are likeliest to contain a person. The combination of the three detection phases reduces false positives, preserving the majority of pedestrians. The system tests conducted in our dataset, which contain low-resolution pedestrians, achieved a maximum performance of 25.5% miss rate with a rate of 10 - 1 false positives per image. This value is comparable to the best detection values for this kind of images. In addition, the processing time is between 2 and 6fps on 640×480 pixel captures. This is therefore a fast and reliable pedestrian detector. HighlightsA Movement Feature Space generates oriented histogram family descriptors.Detection system involves motion detection, hypothesis generation and validation.A cascade of classifiers combine generative and discriminants functions.Best result gives 25.5% of miss rate with 0.1 false positives per image.Running time is between 2 and 6fps in 640×480 frames size.

A min-plus derivation of the fundamental car-traffic law

We give deterministic and stochastic models of the traffic on a circular road without overtaking. From this model the mean speed is derived as an eigenvalue of the min-plus matrix describing the dynamics of the system in the deterministic case and as the Lyapunov exponent of a min-plus stochastic matrix in the stochastic case. The eigenvalue and the Lyapunov exponent are computed explicitly. From these formulas, we derive the fundamental law that links the flow to the density of vehicles on the road. Numerical experiments using the MAXPLUS toolbox of SCILAB confirm the theoretical results obtained.

Stabilization of the Generalized Benders Decomposition applied to Short-Term Hydrothermal Coordination Problem

Solving the Short Term Hydrothermal Coordination (STHTC) Problem considers the resolution of both the Unit Commitment (UC) and the Economic Dispatch (ED) for thermal and hydraulic units. In order to avoid post-dispatch corrections, the transmission network is modeled with a high level of detail considering an AC power flow. These facts lead to a very complex optimization problem which is solved by using a novel decomposition approach which combines Generalized Benders Decomposition (GBD) with Bundle methods presented in [LS97]. This proposed method resembles a stabilized version of the cutting planes method, which drastically reduces the well-known tailing-off effect that Benders methods have. The approach presented in this work allows the decomposition of the whole problem in a quadratic mixed integer master problem, and in a non-linear subproblem which should be separable. The former defines the state and the active power dispatched by each unit whereas the latter determines the reactive power to meet the electrical constraints through a modified AC optimal power flow (OPF). These approaches were applied to a 9-bus test case, and to the IEEE 24-bus test case. The problem is solved for a time horizon of a day with a one-hour step.

Pedestrian Detection Using a Feature Space Based on Colored Level Lines

This work gives the guidelines to develop a pedestrian detection system using a feature space based on colored level lines, called Movement Feature Space (MFS). Besides detecting the movement in the scene, this feature space defines the descriptors used by the classifiers to identify pedestrians. The multi-channel level lines approach has been tested on the HSV color space, which improves the one-channel (gray scale) level lines calculation. Locations hypotheses of pedestrian are performed by a cascade of boosted classifiers. The validation of these regions of interest is carry out by a Support Vector Machine classifier. Results give more than 78.5 % of good detections on urban video sequences.

A heuristic for the OD matrix adjustment problem in a congested transport network

We study the Demand Adjustment Problem (DAP) associated to the urban traffic planning. The framework for the formulation of the DAP is mathematical programming with equilibrium constraints. In particular, if we consider the optimization problem equivalent to the equilibrium problem, the DAP becomes a bilevel optimization problem. In this work we present a descent scheme based on the approximation of the gradient of the objective function of DAP.

Comments on “A Closed-Form Solution to Tensor Voting: Theory and Applications”

We comment on a paper that describes a closed-form formulation to Tensor Voting, a technique to perceptually group clouds of points, usually applied to infer features in images. The authors proved an analytic solution to the technique, a highly relevant contribution considering that the original formulation required numerical integration, a time-consuming task. Their work constitutes the first closed-form expression for the Tensor Voting framework. In this work we first observe that the proposed formulation leads to unexpected results which do not satisfy the constraints for a Tensor Voting output, hence they cannot be interpreted. Given that the closed-form expression is said to be an analytic equivalent solution, unexpected outputs should not be encountered unless there are flaws in the proof. We analyzed the underlying math to find which were the causes of these unexpected results. In this commentary we show that their proposal does not in fact provide a proper analytic solution to Tensor Voting and we indicate the flaws in the proof.

Public Transport Priority for Multimodal Urban Traffic Control

Abstract In order to improve the travel time of surface public transport vehicles (bus, tramway, etc.), several cities use Urban Traffic Control (UTC) systems enabling to give priority to public transport. This paper reviews these systems. Further on after a debate on their insufficiencies in the global regulation of the urban traffic on a whole network, the paper proposes intermodal regulation strategies, operating on intersection traffic lights to regulate the traffic, favouring the public transport. All these strategies are based on the Linear Quadratic (LQ) optimal control theory, but they are different in their ways of taking into account the public transport in the optimization problem. The simulation tests are carried out in a network of eight intersections and two public transport lines.

Solving minimax control problems via nonsmooth optimization

We address minimax optimal control problems with linear dynamics. Under convexity assumptions, by using non-smooth optimization techniques, we derive a set of optimality conditions for the continuous-time case. We define an approximated discrete-time problem where analogous conditions hold. One of them allows us to design an easily implementable descent method. We analyze its convergence and we show some preliminary numerical results.