1,721,152 research outputs found
Image Data Simplification using Spherical and Ellipsoidal Primitives
No full textThis paper discusses the problem of approximating data points in n-dimensional Euclidean space, using spherical and ellipsoidal surfaces. For the specific cases of n = 2 and n = 3, the problem is of fundamental importance id computer vision and robotics. A closed form solution is provided for spherical approximation, while an efficient, globally optimal solution for the ellipsoidal problem is proposed in terms of semidefinite programming (SDP). The paper also presents a result for robust fitting in the presence of outliers, and illustrates the theory with several numerical example
Direct Data-Driven Portfolio Optimization with Guaranteed Shortfall Probability
Full text linkThis paper proposes a novel methodology for optimal allocation of a portfolio of risky financial assets. Most existing methods that aim at compromising between portfolio performance (e.g., expected return) and its risk (e.g., volatility or shortfall probability) need some statistical model of the asset returns. This means that: ({\em i}) one needs to make rather strong assumptions on the market for eliciting a return distribution, and ({\em ii}) the parameters of this distribution need be somehow estimated, which is quite a critical aspect, since optimal portfolios will then depend on the way parameters are estimated. Here we propose instead a direct, data-driven, route to portfolio optimization that avoids both of the mentioned issues: the optimal portfolios are computed directly from historical data, by solving a sequence of convex optimization problems (typically, linear programs). Much more importantly, the resulting portfolios are theoretically backed by a guarantee that their expected shortfall is no larger than an a-priori assigned level. This result is here obtained assuming efficiency of the market, under no hypotheses on the shape of the joint distribution of the asset returns, which can remain unknown and need not be estimate
Parallel block coordinate minimization with application to group regularized regression
Full text linkThis paper proposes a method for parallel block coordinate-wise minimization of convex functions. Each iteration involves a first phase where n independent minimizations are performed over the n variable blocks, followed by a phase where the results of the first phase are coordinated to obtain the whole variable update. Convergence of the method to the global optimum is proved for functions composed of a smooth part plus a possibly non-smooth but separable term. The method is also proved to have a linear rate of convergence, for functions that are smooth and strongly convex. The proposed algorithm can give computational advantage over the more standard serial block coordinate-wise minimization methods, when run over a parallel, multi-worker, computing architecture. The method is suitable for regularized regression problems, such as the group Lasso, group Ridge regression, and group Elastic Net. Numerical tests are run on such types of regression problems to exemplify the performance of the proposed metho
Orthotopic and Ellipsoidal Simulations for a Class of Non-Linear Systems
No full textIn this paper, we address the problem of propagating in time an orthotopic or ellipsoidal bounding set for the state of discrete-time quadratic systems. The sequence of bounding sets is called the set simulation of the system, and conveys useful information about the stability and other qualitative behaviors of the possible trajectories of the system. The bounding sets are computed recursively via numerically efficient algorithms
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