444,976 research outputs found

    Manifold Optimization Over the Set of Doubly Stochastic Matrices: A Second-Order Geometry

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    Convex optimization is a well-established research area with applications in almost all fields. Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a more general set of convex programs known as semi-definite programs and second-order cone programs. However, it has been established that these methods are excessively slow for high dimensions, i.e., they suffer from the curse of dimensionality. On the other hand, optimization algorithms on manifold have shown great ability in finding solutions to nonconvex problems in reasonable time. This paper is interested in solving a subset of convex optimization using a different approach. The main idea behind Riemannian optimization is to view the constrained optimization problem as an unconstrained one over a restricted search space. The paper introduces three manifolds to solve convex programs under particular box constraints. The manifolds, called the doubly stochastic, symmetric and the definite multinomial manifolds, generalize the simplex also known as the multinomial manifold. The proposed manifolds and algorithms are well-adapted to solving convex programs in which the variable of interest is a multidimensional probability distribution function. Theoretical analysis and simulation results testify the efficiency of the proposed method over state of the art methods. In particular, they reveal that the proposed framework outperforms conventional generic and specialized solvers, especially in high dimensions

    The role of the discrete-time Kalman-Yakubovitch-Popov lemma in designing statistically optimum FIR orthonormal filter banks

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    We introduce a new approach to design FIR energy compaction filters of arbitrary order N. The optimization of such filters is important due to their close connection to the design of an M-channel orthonormal filter bank adapted to the input signal statistics. The novel procedure finds the optimum product filter Fopt(Z)=H opt(Z)Hopt(Z^-1) corresponding to the compaction filter Hopt(z). The idea is to express F(z) as D(z)+D(z^-1) and reformulate the compaction problem in terms of the state space realization of the causal function D(z). For a fixed input power spectrum, the resulting filter Fopt(z) is guaranteed to be a global optimum due to the convexity of the new formulation. The new design method can be solved quite efficiently and with great accuracy using recently developed interior point methods and is extremely general in the sense that it works for any chosen M and any arbitrary filter length N. Finally, obtaining Hopt(z) from F opt(z) does not require an additional spectral factorization step. The minimum phase spectral factor can be obtained automatically by relating the state space realization of Dopt(z) to that of H opt(z)

    A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks

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    This paper proposes a quadratic convex model for optimal operation of battery energy storage systems in a direct current (DC) network that approximates the original nonlinear non-convex one. The proposed quadratic convex model uses Taylor’s series expansion to transform the product between voltage variables in the power balance equations into a linear combination of them. Numerical simulations in the general algebraic modeling system (GAMS) for both models show small diferences in the daily energy losses, which are lower than 3.00%. The main advantage of the proposed quadratic model is that its optimal solution is achievable with interior point methods guaranteeing its uniqueness (convexity properties of the solution space and objective function), which is not possible to guarantee with the exact nonlinear non-convex model. The 30-bus DC test feeder with four distributed generators (with power generation forecast via artifcial neural networks with errors lower than 1% between real and predicted generation curves) and three batteries is used to validate the proposed convex and exact models. Numerical results obtained by GAMS show the efectiveness of the proposed quadratic convex model for diferent simulation scenarios tested, which was confrmed by the CVX tool for convex optimization in MATLA

    Interior Pracimayasa Di Pura Mangkunegaran Surakarta (Kajian Estetik) = The Pracimayasa Interior at Pura Mangkunegaran Surakarta (Esthetics Research)

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    ABSTRACT The title of this research is "The Pracimayasa Interior at Pura Mangkunegaran Surakarta." The objectives of this research are: (1) to understand the background of how the Pracimayasa interior came into existence and its function in relation to the designer\u27s point of view, that is Mangkunegara VII(2) to trace the artistic of Pracimayasa interior in connection with Javanese ethical values. Since the Pracimayasa interior is a cultural work that was designed by Mangkunegara VII, this research focuses on its historical perspective based on an assumption that a work of art is the result of the artist\u27s creativity where at the same time it is also an indication of a behavioral change. This research borrows R.M. Soedarsono\u27s concept that a change motivated is triggered by two factors, that are, internal factors and external factors. In directing to a proper interpretation, this study also borrows Monroe C. Beardsley\u27s theory which says that a work of art is said to have artistic values if it contains three elements: (1) unity, (2) complexity, and (3) intensity. To obtain a more comprehensive and substantial answer, this research has applied a qualitative approach and is supported by other approaches from several social sciences. The methods which are used are literary study, observation, and interviews. The result of this research shows that the materialized background of Pracimayasa interior is encouraged by internal and external factors. The internal factor was based on the Mangkunegara VII\u27s need to legitimized to the power, to respect Gusti Ratu Timur\u27s father who would be his father-in-law (Gusti Ratu Timur was Mangkunegara VII\u27s consort), the movement that was initiated by Java Instituut, and the progressive modern way of thinking about the particularity of space. The external factor was based on his political cooperation and alliance with the Dutch colonial Government and his western educational background. There are three prominent artistic elements of the Pracimayasa interior: (1) the harmonious unity in the arrangement of the interior elements of every room, (2) his ideas and courage to insert ancient Javanese traditional element mixed with luxurious Western cultural arts which applied modern techniques which consequently result in a diversity of art works, and (3) the intensity of power the standardization of non-verbal elements of Javanese etiquette as the soul of planning Keywords: interior, power, etiquette value, and spirit/soul

    Bundle-based pruning in the max-plus curse of dimensionality free method

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    Recently a new class of techniques termed the max-plus curse of dimensionality-free methods have been developed to solve nonlinear optimal control problems. In these methods the discretization in state space is avoided by using a max-plus basis expansion of the value function. This requires storing only the coefficients of the basis functions used for representation. However, the number of basis functions grows exponentially with respect to the number of time steps of propagation to the time horizon of the control problem. This so called "curse of complexity" can be managed by applying a pruning procedure which selects the subset of basis functions that contribute most to the approximation of the value function. The pruning procedures described thus far in the literature rely on the solution of a sequence of high dimensional optimization problems which can become computationally expensive. In this paper we show that if the max-plus basis functions are linear and the region of interest in state space is convex, the pruning problem can be efficiently solved by the bundle method. This approach combining the bundle method and semidefinite formulations is applied to the quantum gate synthesis problem, in which the state space is the special unitary group (which is non-convex). This is based on the observation that the convexification of the unitary group leads to an exact relaxation. The results are studied and validated via examples

    Two triangulations methods based on edge refinement

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    In this paper two curvature adaptive methods of surface triangulation are presented. Both methods are based on edge refinement to obtain a triangulation compatible with the curvature requirements. The first method applies an incremental and constrained Delaunay triangulation and uses curvature bounds to determine if an edge of the triangulation is admissible. The second method uses this function also in the edge refinement process, i.e. in the computation of the location of a refining point, and in the re-triangulation needed after the insertion of this refining point. Results are presented, comparing both approachesPostprint (published version
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