Conic Linear Programming

Luenberger, David G.; Ye, Yinyu

doi:10.1007/978-3-319-18842-3_6

Cited by 320 publications

(483 citation statements)

References 32 publications

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“…The minimization problem of (10) was solved using the quasi-Newton optimization technique [22] because it does not require the calculation of the Hessian, and hence fast. The initial vectors taken for the optimization were the columns of the identity matrix, that is Φ = I.…”

Section: Resultsmentioning

confidence: 99%

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Transform learning algorithm based on the probability of representation of signals

Parthasarathy

Abhilash

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-Compressed sensing is a signal acquisition scheme that measures signals at sub-Nyquist rate amenable to sparse recovery, with high probability, from a reduced set of measurements. One of the main requirements of compressive sensing is the sparsity of the class of signals of interest in some basis. A method to construct a sparsifying basis for a class of signals using information theoretic measures is proposed in this paper. The algorithm constructs the sparsifying basis from a known nonsparsifying basis by concentrating the probability distribution of the basis in the representation of a class of signals. Simulation studies using speech and image signals confirm that the basis constructed using the proposed method results in an improved sparsity of the signals with thresholded coefficients but without degrading the signal quality.

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Section: Resultsmentioning

confidence: 99%

“…We have chosen the quasi-Newton method [22] to carry out the minimization in (10), the convergence of which is well known. To establish the convergence of the proposed algorithm as a whole, we define the error terms of (10) at the end of the i-th iteration as…”

Section: B Convergencementioning

confidence: 99%

Transform learning algorithm based on the probability of representation of signals

Parthasarathy

Abhilash

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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“…To ensure that the gradient step respects the constraints on α (α d ≥ 0 and d α d = 1), the following strategy is used: similarly to [47,48,45], the…”

Section: : End Formentioning

confidence: 99%

On-line relational and multiple relational SOM

Olteanu¹,

Villa-Vialaneix²

2015

Neurocomputing

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In some applications and in order to address real-world situations better, data may be more complex than simple numerical vectors. In some examples, data can be known only through their pairwise dissimilarities or through multiple dissimilarities, each of them describing a particular feature of the data set. Several variants of the Self Organizing Map (SOM) algorithm were introduced to generalize the original algorithm to the framework of dissimilarity data. Whereas median SOM is based on a rough representation of the prototypes, relational SOM allows representing these prototypes by a virtual linear combination of all elements in the data set, referring to a pseudo-euclidean framework. In the present article, an on-line version of relational SOM is introduced and studied. Similarly to the situation in the Euclidean framework, this on-line algorithm provides a better organization and is much less sensible to prototype initialization than standard (batch) relational SOM. In a more general case, this stochastic version allows us to integrate an additional stochastic gradient descent step in the algorithm which can tune the respective weights of several dissimilarities in an optimal way: the resulting multiple relational SOM thus has the ability to integrate several sources of data of different types, or to make a consensus between several dissimilarities describing the same data. The algorithms introduced in this manuscript are tested on several data sets, including categorical data and graphs. On-line relational SOM is currently available in the R package SOMbrero that can be downloaded at http://sombrero.r-forge.r-project.org/ or directly tested on its Web User Interface at http://shiny.nathalievilla.org/sombrero.

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“…In this case, the integrand is known explicitly throughout the integral since all the terms in (6) are known explicitly in terms of P from the joint angles q = q(t, P ). Given J(P ) and its gradient, we could easily minimize it over P using Matlab's BFGS [9] algorithm in the function "fminunc." Figure 3 shows the locally optimal solution found to this problem using the parameter optimization approach mentioned above.…”

Section: Case 1: Fully Actuated Robotmentioning

confidence: 99%

“…In addition to this example, we have used this basic approach to solve for much more complex optimal high-dive motions for a human-like diver in [16]. When we computed the above solution to the underactuated Acrobot, we did not expect numerical difficulties, since we had the exact gradient of the objective function and the optimization algorithm has well-established convergence properties for this case [9]. However, we did encounter some numerical problems and had to adjust some of the tolerances in the optimizer in order to achieve convergence, and the computation time, even in the best of cases (about 5 minutes on a PIII-800 PC), was much longer than in the previous example.…”

Section: Case 2: Underactuated Robotmentioning

confidence: 99%

Recent Advances on the Algorithmic Optimization of Robot Motion

Bobrow

Park

Sideris

Lecture Notes in Control and Information Sciences

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Summary. An important technique for computing motions for robot systems is to conduct a numerical search for a trajectory that minimizes a physical criteria like energy, control effort, jerk, or time. In this paper, we provide example solutions of these types of optimal control problems, and develop a framework to solve these problems reliably. Our approach uses an efficient solver for both inverse and forward dynamics along with the sensitivity of these quantities used to compute gradients, and a reliable optimal control solver. We give an overview of our algorithms for these elements in this paper. The optimal control solver has been the primary focus of our recent work. This algorithm creates optimal motions in a numerically stable and efficient manner. Similar to sequential quadratic programming for solving finite-dimensional optimization problems, our approach solves the infinite-dimensional problem using a sequence of linear-quadratic optimal control subproblems. Each subproblem is solved efficiently and reliably using the Riccati differential equation.

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Conic Linear Programming

Cited by 320 publications

References 32 publications

Transform learning algorithm based on the probability of representation of signals

Transform learning algorithm based on the probability of representation of signals

On-line relational and multiple relational SOM

Recent Advances on the Algorithmic Optimization of Robot Motion

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