The Experts below are selected from a list of 84 Experts worldwide ranked by ideXlab platform

Rida T. Farouki - One of the best experts on this subject based on the ideXlab platform.

  • Construction ofC ^2 Pythagorean-hodograph interpolating splines by the homotopy method
    Advances in Computational Mathematics, 1996
    Co-Authors: Gudrun Albrecht, Rida T. Farouki
    Abstract:

    The complex Representation of Polynomial Pythagorean-hodograph (PH) curves allows the problem of constructing a C ^2 PH quintic “spline” that interpolates a given sequence of points p _0, p _1,..., p _ N and end-derivatives d _0 and d _ N to be reduced to solving a “tridiagonal” system of N quadratic equations in N complex unknowns. The system can also be easily modified to incorporate PH-spline end conditions that bypass the need to specify end-derivatives. Homotopy methods have been employed to compute all solutions of this system, and hence to construct a total of 2^ N +1 distinct interpolants for each of several different data sets. We observe empirically that all but one of these interpolants exhibits undesirable “looping” behavior (which may be quantified in terms of the elastic bending energy , i.e., the integral of the square of the curvature with respect to arc length). The remaining “good” interpolant, however, is invariably a fairer curve-having a smaller energy and a more even curvature distribution over its extent-than the corresponding “ordinary” C _2 cubic spline. Moreover, the PH spline has the advantage that its offsets are rational curves and its arc length is a Polynomial function of the curve parameter.

  • construction of c 2 pythagorean hodograph interpolating splines by the homotopy method
    Advances in Computational Mathematics, 1996
    Co-Authors: Gudrun Albrecht, Rida T. Farouki
    Abstract:

    The complex Representation of Polynomial Pythagorean-hodograph (PH) curves allows the problem of constructing a C 2 PH quintic "'spline" that interpolates a given sequence of points P0, Pt,.-., Pu and end-derivatives d o and du to be reduced to solving a "tridiagonal" system of N quadratic equations in N complex unknowns. The system can also be easily modified to incorporate PH-spline end conditions that bypass the need to specify end-derivatives. Homotopy methods have been employed to compute all solutions of this system, and hence to construct a total of 2 ~+~ distinct interpolants for each of several different data sets. We observe empirically that all but one of these interpolants exhibits undesirable "looping" behavior (which may be quantified in terms of the elastic bending energy, i.e., the integral of the square of the curvature with respect to arc length). The remaining "good" interpolant, however, is invariably a fairer curve-having a smaller energy and a more even curvature distribution over its extent-than the corresponding "ordinary" C 2 cubic spline. Moreover, the PH spline has the advantage that its offsets are rational curves and its arc length is a Polynomial function of the curve parameter.

  • Construction ofC 2 Pythagorean-hodograph interpolating splines by the homotopy method
    Advances in Computational Mathematics, 1996
    Co-Authors: Gudrun Albrecht, Rida T. Farouki
    Abstract:

    The complex Representation of Polynomial Pythagorean-hodograph (PH) curves allows the problem of constructing a C 2 PH quintic "spline" that interpolates a given sequence of points p 0 , p 1 , ⋯ p N and end - derivatives d 0 and d N to be reduced to solving a "tridiagonal" system of N quadratic equations in N complex unknowns. The system can also be easily modified to incorporate PH - spline end conditions that bypass the need to specify end - derivatives. Homotopy methods have been employed to compute all solutions of this system, and hence to construct a total of 2 N+1 distinct interpolants for each of several different data sets. We observe empirically that all but one of these interpolants exhibits undesirable "looping" behavior (which may be quantified in terms of the elastic bending energy, i.e., the integral of the square of the curvature with respect to arc length). The remaining "good" interpolant, however, is invariably a fairer curve-having a smaller energy and a more even curvature distribution over its extent-than the corresponding "ordinary" C 2 cubic spline. Moreover, the PH spline has the advantage that its offsets are rational curves and its arc length is a Polynomial function of the curve parameter. © J.C. Baltzer AG, Science Publishers.

Emiliano Traversi - One of the best experts on this subject based on the ideXlab platform.

  • A Julia Module for Polynomial Optimization with Complex Variables applied to Optimal Power Flow
    2019 IEEE Milan PowerTech, 2019
    Co-Authors: Julie Sliwak, Manuel Ruiz, Miguel F. Anjos, Lucas Létocart, Emiliano Traversi
    Abstract:

    Many optimization problems in power transmission networks can be formulated as Polynomial problems with complex variables. A Polynomial optimization problem with complex variables consists in optimizing a real-valued Polynomial whose variables and coefficients are complex numbers subject to some complex Polynomial equality or inequality constraints. These problems are usually directly expressed with real variables. In this work, we propose a Julia module allowing the Representation of Polynomial problems in their original complex formulation. This module is applied to power system optimization and its generic design enables the description of several variants of power system problems. Results for the Optimal Power Flow in Alternating Current problem and for the Preventive-Security Constrained Optimal Power Flow problem are presented.

  • A Julia Module for Polynomial Optimization with Complex Variables applied to Optimal Power Flow
    arXiv: Optimization and Control, 2019
    Co-Authors: Julie Sliwak, Manuel Ruiz, Miguel F. Anjos, Lucas Létocart, Emiliano Traversi
    Abstract:

    Many optimization problems in power transmission networks can be formulated as Polynomial problems with complex variables. A Polynomial optimization problem with complex variables consists in optimizing a real-valued Polynomial whose variables and coefficients are complex numbers subject to some complex Polynomial equality or inequality constraints. These problems are usually directly converted to real variables, either using the polar form or the rectangular form. In this work, we propose a Julia module allowing the Representation of Polynomial problems in their original complex formulation. This module is applied to power systems optimization and its generic design enables the description of several variants of power system problems. Results for the Optimal Power Flow in Alternating Current problem and for the Preventive-Security Constrained Optimal Power Flow problem are presented.

Gudrun Albrecht - One of the best experts on this subject based on the ideXlab platform.

  • Construction ofC ^2 Pythagorean-hodograph interpolating splines by the homotopy method
    Advances in Computational Mathematics, 1996
    Co-Authors: Gudrun Albrecht, Rida T. Farouki
    Abstract:

    The complex Representation of Polynomial Pythagorean-hodograph (PH) curves allows the problem of constructing a C ^2 PH quintic “spline” that interpolates a given sequence of points p _0, p _1,..., p _ N and end-derivatives d _0 and d _ N to be reduced to solving a “tridiagonal” system of N quadratic equations in N complex unknowns. The system can also be easily modified to incorporate PH-spline end conditions that bypass the need to specify end-derivatives. Homotopy methods have been employed to compute all solutions of this system, and hence to construct a total of 2^ N +1 distinct interpolants for each of several different data sets. We observe empirically that all but one of these interpolants exhibits undesirable “looping” behavior (which may be quantified in terms of the elastic bending energy , i.e., the integral of the square of the curvature with respect to arc length). The remaining “good” interpolant, however, is invariably a fairer curve-having a smaller energy and a more even curvature distribution over its extent-than the corresponding “ordinary” C _2 cubic spline. Moreover, the PH spline has the advantage that its offsets are rational curves and its arc length is a Polynomial function of the curve parameter.

  • construction of c 2 pythagorean hodograph interpolating splines by the homotopy method
    Advances in Computational Mathematics, 1996
    Co-Authors: Gudrun Albrecht, Rida T. Farouki
    Abstract:

    The complex Representation of Polynomial Pythagorean-hodograph (PH) curves allows the problem of constructing a C 2 PH quintic "'spline" that interpolates a given sequence of points P0, Pt,.-., Pu and end-derivatives d o and du to be reduced to solving a "tridiagonal" system of N quadratic equations in N complex unknowns. The system can also be easily modified to incorporate PH-spline end conditions that bypass the need to specify end-derivatives. Homotopy methods have been employed to compute all solutions of this system, and hence to construct a total of 2 ~+~ distinct interpolants for each of several different data sets. We observe empirically that all but one of these interpolants exhibits undesirable "looping" behavior (which may be quantified in terms of the elastic bending energy, i.e., the integral of the square of the curvature with respect to arc length). The remaining "good" interpolant, however, is invariably a fairer curve-having a smaller energy and a more even curvature distribution over its extent-than the corresponding "ordinary" C 2 cubic spline. Moreover, the PH spline has the advantage that its offsets are rational curves and its arc length is a Polynomial function of the curve parameter.

  • Construction ofC 2 Pythagorean-hodograph interpolating splines by the homotopy method
    Advances in Computational Mathematics, 1996
    Co-Authors: Gudrun Albrecht, Rida T. Farouki
    Abstract:

    The complex Representation of Polynomial Pythagorean-hodograph (PH) curves allows the problem of constructing a C 2 PH quintic "spline" that interpolates a given sequence of points p 0 , p 1 , ⋯ p N and end - derivatives d 0 and d N to be reduced to solving a "tridiagonal" system of N quadratic equations in N complex unknowns. The system can also be easily modified to incorporate PH - spline end conditions that bypass the need to specify end - derivatives. Homotopy methods have been employed to compute all solutions of this system, and hence to construct a total of 2 N+1 distinct interpolants for each of several different data sets. We observe empirically that all but one of these interpolants exhibits undesirable "looping" behavior (which may be quantified in terms of the elastic bending energy, i.e., the integral of the square of the curvature with respect to arc length). The remaining "good" interpolant, however, is invariably a fairer curve-having a smaller energy and a more even curvature distribution over its extent-than the corresponding "ordinary" C 2 cubic spline. Moreover, the PH spline has the advantage that its offsets are rational curves and its arc length is a Polynomial function of the curve parameter. © J.C. Baltzer AG, Science Publishers.

Julie Sliwak - One of the best experts on this subject based on the ideXlab platform.

  • A Julia Module for Polynomial Optimization with Complex Variables applied to Optimal Power Flow
    2019 IEEE Milan PowerTech, 2019
    Co-Authors: Julie Sliwak, Manuel Ruiz, Miguel F. Anjos, Lucas Létocart, Emiliano Traversi
    Abstract:

    Many optimization problems in power transmission networks can be formulated as Polynomial problems with complex variables. A Polynomial optimization problem with complex variables consists in optimizing a real-valued Polynomial whose variables and coefficients are complex numbers subject to some complex Polynomial equality or inequality constraints. These problems are usually directly expressed with real variables. In this work, we propose a Julia module allowing the Representation of Polynomial problems in their original complex formulation. This module is applied to power system optimization and its generic design enables the description of several variants of power system problems. Results for the Optimal Power Flow in Alternating Current problem and for the Preventive-Security Constrained Optimal Power Flow problem are presented.

  • A Julia Module for Polynomial Optimization with Complex Variables applied to Optimal Power Flow
    arXiv: Optimization and Control, 2019
    Co-Authors: Julie Sliwak, Manuel Ruiz, Miguel F. Anjos, Lucas Létocart, Emiliano Traversi
    Abstract:

    Many optimization problems in power transmission networks can be formulated as Polynomial problems with complex variables. A Polynomial optimization problem with complex variables consists in optimizing a real-valued Polynomial whose variables and coefficients are complex numbers subject to some complex Polynomial equality or inequality constraints. These problems are usually directly converted to real variables, either using the polar form or the rectangular form. In this work, we propose a Julia module allowing the Representation of Polynomial problems in their original complex formulation. This module is applied to power systems optimization and its generic design enables the description of several variants of power system problems. Results for the Optimal Power Flow in Alternating Current problem and for the Preventive-Security Constrained Optimal Power Flow problem are presented.

Manuel Ruiz - One of the best experts on this subject based on the ideXlab platform.

  • A Julia Module for Polynomial Optimization with Complex Variables applied to Optimal Power Flow
    2019 IEEE Milan PowerTech, 2019
    Co-Authors: Julie Sliwak, Manuel Ruiz, Miguel F. Anjos, Lucas Létocart, Emiliano Traversi
    Abstract:

    Many optimization problems in power transmission networks can be formulated as Polynomial problems with complex variables. A Polynomial optimization problem with complex variables consists in optimizing a real-valued Polynomial whose variables and coefficients are complex numbers subject to some complex Polynomial equality or inequality constraints. These problems are usually directly expressed with real variables. In this work, we propose a Julia module allowing the Representation of Polynomial problems in their original complex formulation. This module is applied to power system optimization and its generic design enables the description of several variants of power system problems. Results for the Optimal Power Flow in Alternating Current problem and for the Preventive-Security Constrained Optimal Power Flow problem are presented.

  • A Julia Module for Polynomial Optimization with Complex Variables applied to Optimal Power Flow
    arXiv: Optimization and Control, 2019
    Co-Authors: Julie Sliwak, Manuel Ruiz, Miguel F. Anjos, Lucas Létocart, Emiliano Traversi
    Abstract:

    Many optimization problems in power transmission networks can be formulated as Polynomial problems with complex variables. A Polynomial optimization problem with complex variables consists in optimizing a real-valued Polynomial whose variables and coefficients are complex numbers subject to some complex Polynomial equality or inequality constraints. These problems are usually directly converted to real variables, either using the polar form or the rectangular form. In this work, we propose a Julia module allowing the Representation of Polynomial problems in their original complex formulation. This module is applied to power systems optimization and its generic design enables the description of several variants of power system problems. Results for the Optimal Power Flow in Alternating Current problem and for the Preventive-Security Constrained Optimal Power Flow problem are presented.