Lp LOSC-Support Vector Machines for Regression Estimation and their Application to Geomatics

<p>The classification of vertical displacements and the estimation of a local geometric geoid model and coordinate transformation were recently solved by the L<sup>2</sup> support vector machine and support vector regression. The L<sup>p</sup> quasi-norm SVM and SVR (0<p<1) is a non-convex and non-Lipschitz optimization problem that has been successfully formulated as an optimization model with a linear objective function and smooth constraints (LOSC) that can be solved by any black-box computing software, e.g., MATLAB, R and Python. The aim of this talk is to show that interior-point based algorithms, when applied correctly, can be effective for handling different LOSC-SVM and LOSC-SVR based models with different p values, in order to obtain better sparsity regularization and feature selection. As a comparative study, some artificial and real-life geoscience datasets are used to test the effectiveness of our proposed methods. Most importantly, the methods presented here can be used in geodetic classroom teaching to benefit our undergraduate students and further bridge the gap between the applications of geomatics and machine learning.</p>

Optimal Pressure Management for Large-Scale Water Distribution Systems Using Smoothing Model

Optimal pressure management in water distribution systems (WDSs) is one of the most efficient approaches to control water leakage for water utilities worldwide. The optimal pressure management can be accomplished through regulating operations of pressure reducing valves (PRVs) to ensure that the excessive pressure in the WDS is minimized. This engineering task can be casted into a nonlinear program problem (NLP) with non-smooth constraints. Until now, the non-smooth constraints have been approximated by the smoothing function of Chen Harker-Kanzow-Smale (CHKS). In this paper, instead of using the CHKS function, we propose to apply the uniform smoothing function for formulation of the NLP. Numerical simulations using two smoothing functions will be carried out for optimal pressure managements of a benchmark WDS and a real-world WDS in Thainguyen City, in Vietnam. The comparison results reveal that the NLP formulated with the uniform smoothing function outperforms the existing NLP formulated with the CHKS in terms of optimal solution accuracy.

Gradient-based Learning Methods Extended to Smooth Manifolds Applied to Automated Clustering

Grassmann manifold based sparse spectral clustering is a classification technique that consists in learning a latent representation of data, formed by a subspace basis, which is sparse. In order to learn a latent representation, spectral clustering is formulated in terms of a loss minimization problem over a smooth manifold known as Grassmannian. Such minimization problem cannot be tackled by one of traditional gradient-based learning algorithms, which are only suitable to perform optimization in absence of constraints among parameters. It is, therefore, necessary to develop specific optimization/learning algorithms that are able to look for a local minimum of a loss function under smooth constraints in an efficient way. Such need calls for manifold optimization methods. In this paper, we extend classical gradient-based learning algorithms on at parameter spaces (from classical gradient descent to adaptive momentum) to curved spaces (smooth manifolds) by means of tools from manifold calculus. We compare clustering performances of these methods and known methods from the scientific literature. The obtained results confirm that the proposed learning algorithms prove lighter in computational complexity than existing ones without detriment in clustering efficacy.

An Asymptotic Numerical Continuation Power Flow to Cope with Non-Smooth Issue

Continuation power flow (CPF) calculation is very important for analyzing voltage stability of power system. CPF calculation needs to deal with non-smooth constraints such as the generator buses reactive power limits. It is still a technical challenge to determine the step size while dealing with above non-smooth constraints in CPF calculation. In this paper, an asymptotic numerical method (ANM) based on Fischer‐Burmeister (FB) function, is proposed to calculate CPF. We first used complementarity constraints to cope with non-smooth issues and introduced the FB function to formulate the complementarity constraints. Meanwhile, we introduced new variables for substitution to meet the quadratic function requirements of ANM. Compared with the conventional predictor-corrector method combining with heuristic PV-PQ (PV and PQ are used to describe bus types. PV means that the active power and voltage of the bus are known. PQ means that the active and reactive power of bus are known.) bus type switching, ANM can effectively solve the PV-PQ bus type switching problem in CPF calculation. Furthermore, to assure high efficiency, ANM can rapidly approach the voltage collapse point by self-adaptive step size adjustment and constant Jacobian matrix used for power series expansion. However, conventional CPF needs proper step set in advance and calculates Jacobian matrix for each iteration. Numerical tests on a nine-bus network and a 182-bus network validate that the proposed method is more robust than existing methods.

LAGRANGIAN SYSTEMS WITH NON-SMOOTH CONSTRAINTS

The Lagrange-d'Alembert equations with constraints belonging to H1,∞ have been considered. A concept of weak solutions to these equations has been built. A global existence theorem for Cauchy problem has been obtained.