The Experts below are selected from a list of 21216 Experts worldwide ranked by ideXlab platform
Jiming Chen - One of the best experts on this subject based on the ideXlab platform.
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stochastic Steepest Descent optimization of multiple objective mobile sensor coverage
IEEE Transactions on Vehicular Technology, 2012Co-Authors: Chris Y T, David K Y Yau, Nung Kwan Yip, Nageswara S V Rao, Jiming ChenAbstract:We propose a Steepest Descent method to compute optimal control parameters for balancing between multiple performance objectives in stateless stochastic scheduling, wherein the scheduling decision is effected by a simple constant-time coin toss operation only. We apply our method to the scheduling of a mobile sensor's coverage time among a set of points of interest (PoIs). The coverage algorithm is guided by a Markov chain, wherein the sensor at PoI i decides to go to the next PoI j with transition probability pij. We use Steepest Descent to compute the transition probabilities for optimal tradeoff among different performance goals with regard to the distributions of per-PoI coverage times and exposure times and the entropy and energy efficiency of sensor movement. For computational efficiency, we show how we can optimally adapt the step size in Steepest Descent to achieve fast convergence. However, we found that the structure of our problem is complex, because there may exist surprisingly many local optima in the solution space, causing basic Steepest Descent to easily get stuck at a local optimum. To solve the problem, we show how proper incorporation of noise in the search process can get us out of the local optima with high probability. We provide simulation results to verify the accuracy of our analysis and show that our method can converge to the globally optimal control parameters under different assigned weights to the performance goals and different initial parameters.
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stochastic Steepest Descent optimization of multiple objective mobile sensor coverage
International Conference on Distributed Computing Systems, 2010Co-Authors: Chris Y T, David K Y Yau, Nung Kwan Yip, Nageswara S V Rao, Jiming ChenAbstract:We propose a Steepest Descent method to compute optimal control parameters for balancing between multiple performance objectives in stateless stochastic scheduling, wherein the scheduling decision is effected by a simple constant-time coin toss operation only. We apply our method to the scheduling of a mobile sensor’s coverage time among a set of points of interest (PoIs). The coverage algorithm is guided by a Markov chain wherein the sensor at PoI i decides to go to the next PoI j with transition probability pij . We use Steepest Descent to compute the transition probabilities for optimal tradeoff between two performance goals concerning the distributions of per-PoI coverage times and exposure times, respectively. We also discuss how other important goals such as energy efficiency and entropy of the coverage schedule can be addressed. For computational efficiency, we show how to optimally adapt the step size in Steepest Descent to achieve fast convergence. However, we found that the structure of our problem is complex in that there may exist surprisingly many local optima in the solution space, causing basic Steepest Descent to get stuck easily at a local optimum. To solve the problem, we show how proper incorporation of noise in the search process can get us out of the local optima with high probability. We provide simulation results to verify the accuracy of our analysis, and show that our method can converge to the globally optimal control parameters under different assigned weights to the performance goals and different initial parameters.
Klaus Ruedenberg - One of the best experts on this subject based on the ideXlab platform.
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Gradient extremals and Steepest Descent lines on potential energy surfaces
The Journal of Chemical Physics, 1993Co-Authors: Jun‐qiang Sun, Klaus RuedenbergAbstract:Relationships between Steepest Descent lines and gradient extremals on potential surfaces are elucidated. It is shown that gradient extremals are the curves which connect those points where the Steepest Descent lines have zero curvature. This condition gives rise to a direct method for the global determination of gradient extremals which is illustrated on the Muller–Brown surface. Furthermore, explicit expressions are obtained for the derivatives of the Steepest‐Descent‐line curvatures and, from them, for the gradient extremal tangents. With the help of these formulas, a new gradient extremal following algorithm is formulated.
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Quadratic Steepest Descent on potential energy surfaces. III. Minima seeking along Steepest Descent lines
The Journal of Chemical Physics, 1993Co-Authors: Jun‐qiang Sun, Klaus Ruedenberg, Gregory J. AtchityAbstract:A simplified quadratic Steepest Descent method, based on the availability of energies and gradients, is formulated for use in minimum searching. It requires only a fraction of the computational effort needed for the previously developed accurate Steepest Descent procedures and, typically, involves less work than standard quasi‐Newton minimum searches. At the same time, it follows the true Steepest Descent curves reasonably closely and reaches the closest minima. This is in contrast to quasi‐Newton procedures which cannot be relied upon to do so. The performance is documented by applications to a variety of searches on the Muller–Brown surface.
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Quadratic Steepest Descent on potential energy surfaces. I. Basic formalism and quantitative assessment
The Journal of Chemical Physics, 1993Co-Authors: Jun‐qiang Sun, Klaus RuedenbergAbstract:A novel second‐order algorithm is formulated for determining Steepest‐Descent lines on potential energy surfaces. The reaction path is deduced from successive exact Steepest‐Descent lines of local quadratic approximations to the surface. At each step, a distinction is made between three points: the center for the local quadratic Taylor expansion of the surface, the junction of the two adjacent local Steepest‐Descent line approximations, and the predicted approximation to the true Steepest‐Descent line. This flexibility returns a more efficient yield from the calculated information and increases the accuracy of the local quadratic approximations by almost an order of magnitude. In addition, the step size is varied with the curvature and, if desired, can be readjusted by a trust region assessment. Applications to the Gonzalez–Schlegel and the Muller–Brown surfaces show the method to compare favorably with existing methods. Several measures are given for assessing the accuracy achieved without knowledge of the exact Steepest‐Descent line. The optimal evaluation of the predicted gradient and curvature for dynamical applications is discussed.
Lu-chuan Ceng - One of the best experts on this subject based on the ideXlab platform.
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Steepest-Descent Approach to Triple Hierarchical Constrained Optimization Problems
Abstract and Applied Analysis, 2014Co-Authors: Lu-chuan Ceng, Cheng-wen Liao, Chin-tzong Pang, Ching-feng WenAbstract:We introduce and analyze a hybrid Steepest-Descent algorithm by combining Korpelevich’s extragradient method, the Steepest-Descent method, and the averaged mapping approach to the gradient-projection algorithm. It is proven that under appropriate assumptions, the proposed algorithm converges strongly to the unique solution of a triple hierarchical constrained optimization problem (THCOP) over the common fixed point set of finitely many nonexpansive mappings, with constraints of finitely many generalized mixed equilibrium problems (GMEPs), finitely many variational inclusions, and a convex minimization problem (CMP) in a real Hilbert space.
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Mann-Type Steepest-Descent and Modified Hybrid Steepest-Descent Methods for Variational Inequalities in Banach Spaces
Numerical Functional Analysis and Optimization, 2008Co-Authors: Lu-chuan Ceng, Qamrul Hasan Ansari, Jen-chih YaoAbstract:In this paper, we propose three different kinds of iteration schemes to compute the approximate solutions of variational inequalities in the setting of Banach spaces. First, we suggest Mann-type Steepest-Descent iterative algorithm, which is based on two well-known methods: Mann iterative method and Steepest-Descent method. Second, we introduce modified hybrid Steepest-Descent iterative algorithm. Third, we propose modified hybrid Steepest-Descent iterative algorithm by using the resolvent operator. For the first two cases, we prove the convergence of sequences generated by the proposed algorithms to a solution of a variational inequality in the setting of Banach spaces. For the third case, we prove the convergence of the iterative sequence generated by the proposed algorithm to a zero of an operator, which is also a solution of a variational inequality.
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A hybrid Steepest-Descent method for variational inequalities in Hilbert spaces
Applicable Analysis, 2008Co-Authors: Lu-chuan Ceng, Jen-chih YaoAbstract:A Mann-type hybrid Steepest-Descent method for solving the variational inequality ⟨F(u*), v − u*⟩ ≥ 0, v ∈ C is proposed, where F is a Lipschitzian and strong monotone operator in a real Hilbert space H and C is the intersection of the fixed point sets of finitely many non-expansive mappings in H. This method combines the well-known Mann's fixed point method with the hybrid Steepest-Descent method. Strong convergence theorems for this method are established, which extend and improve certain corresponding results in recent literature, for instance, Yamada (The hybrid Steepest-Descent method for variational inequality problems over the intersection of the fixed-point sets of nonexpansive mappings, in Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, D. Butnariu, Y. Censor, and S. Reich, eds., North-Holland, Amsterdam, Holland, 2001, pp. 473–504), Xu and Kim (Convergence of hybrid Steepest-Descent methods for variational inequalities, J. Optim. Theor. Appl. 119 (2003), pp...
Jun‐qiang Sun - One of the best experts on this subject based on the ideXlab platform.
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Gradient extremals and Steepest Descent lines on potential energy surfaces
The Journal of Chemical Physics, 1993Co-Authors: Jun‐qiang Sun, Klaus RuedenbergAbstract:Relationships between Steepest Descent lines and gradient extremals on potential surfaces are elucidated. It is shown that gradient extremals are the curves which connect those points where the Steepest Descent lines have zero curvature. This condition gives rise to a direct method for the global determination of gradient extremals which is illustrated on the Muller–Brown surface. Furthermore, explicit expressions are obtained for the derivatives of the Steepest‐Descent‐line curvatures and, from them, for the gradient extremal tangents. With the help of these formulas, a new gradient extremal following algorithm is formulated.
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Quadratic Steepest Descent on potential energy surfaces. III. Minima seeking along Steepest Descent lines
The Journal of Chemical Physics, 1993Co-Authors: Jun‐qiang Sun, Klaus Ruedenberg, Gregory J. AtchityAbstract:A simplified quadratic Steepest Descent method, based on the availability of energies and gradients, is formulated for use in minimum searching. It requires only a fraction of the computational effort needed for the previously developed accurate Steepest Descent procedures and, typically, involves less work than standard quasi‐Newton minimum searches. At the same time, it follows the true Steepest Descent curves reasonably closely and reaches the closest minima. This is in contrast to quasi‐Newton procedures which cannot be relied upon to do so. The performance is documented by applications to a variety of searches on the Muller–Brown surface.
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Quadratic Steepest Descent on potential energy surfaces. I. Basic formalism and quantitative assessment
The Journal of Chemical Physics, 1993Co-Authors: Jun‐qiang Sun, Klaus RuedenbergAbstract:A novel second‐order algorithm is formulated for determining Steepest‐Descent lines on potential energy surfaces. The reaction path is deduced from successive exact Steepest‐Descent lines of local quadratic approximations to the surface. At each step, a distinction is made between three points: the center for the local quadratic Taylor expansion of the surface, the junction of the two adjacent local Steepest‐Descent line approximations, and the predicted approximation to the true Steepest‐Descent line. This flexibility returns a more efficient yield from the calculated information and increases the accuracy of the local quadratic approximations by almost an order of magnitude. In addition, the step size is varied with the curvature and, if desired, can be readjusted by a trust region assessment. Applications to the Gonzalez–Schlegel and the Muller–Brown surfaces show the method to compare favorably with existing methods. Several measures are given for assessing the accuracy achieved without knowledge of the exact Steepest‐Descent line. The optimal evaluation of the predicted gradient and curvature for dynamical applications is discussed.
Chris Y T - One of the best experts on this subject based on the ideXlab platform.
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stochastic Steepest Descent optimization of multiple objective mobile sensor coverage
IEEE Transactions on Vehicular Technology, 2012Co-Authors: Chris Y T, David K Y Yau, Nung Kwan Yip, Nageswara S V Rao, Jiming ChenAbstract:We propose a Steepest Descent method to compute optimal control parameters for balancing between multiple performance objectives in stateless stochastic scheduling, wherein the scheduling decision is effected by a simple constant-time coin toss operation only. We apply our method to the scheduling of a mobile sensor's coverage time among a set of points of interest (PoIs). The coverage algorithm is guided by a Markov chain, wherein the sensor at PoI i decides to go to the next PoI j with transition probability pij. We use Steepest Descent to compute the transition probabilities for optimal tradeoff among different performance goals with regard to the distributions of per-PoI coverage times and exposure times and the entropy and energy efficiency of sensor movement. For computational efficiency, we show how we can optimally adapt the step size in Steepest Descent to achieve fast convergence. However, we found that the structure of our problem is complex, because there may exist surprisingly many local optima in the solution space, causing basic Steepest Descent to easily get stuck at a local optimum. To solve the problem, we show how proper incorporation of noise in the search process can get us out of the local optima with high probability. We provide simulation results to verify the accuracy of our analysis and show that our method can converge to the globally optimal control parameters under different assigned weights to the performance goals and different initial parameters.
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stochastic Steepest Descent optimization of multiple objective mobile sensor coverage
International Conference on Distributed Computing Systems, 2010Co-Authors: Chris Y T, David K Y Yau, Nung Kwan Yip, Nageswara S V Rao, Jiming ChenAbstract:We propose a Steepest Descent method to compute optimal control parameters for balancing between multiple performance objectives in stateless stochastic scheduling, wherein the scheduling decision is effected by a simple constant-time coin toss operation only. We apply our method to the scheduling of a mobile sensor’s coverage time among a set of points of interest (PoIs). The coverage algorithm is guided by a Markov chain wherein the sensor at PoI i decides to go to the next PoI j with transition probability pij . We use Steepest Descent to compute the transition probabilities for optimal tradeoff between two performance goals concerning the distributions of per-PoI coverage times and exposure times, respectively. We also discuss how other important goals such as energy efficiency and entropy of the coverage schedule can be addressed. For computational efficiency, we show how to optimally adapt the step size in Steepest Descent to achieve fast convergence. However, we found that the structure of our problem is complex in that there may exist surprisingly many local optima in the solution space, causing basic Steepest Descent to get stuck easily at a local optimum. To solve the problem, we show how proper incorporation of noise in the search process can get us out of the local optima with high probability. We provide simulation results to verify the accuracy of our analysis, and show that our method can converge to the globally optimal control parameters under different assigned weights to the performance goals and different initial parameters.
