Solving fractional differential equations by the ultraspherical integration method

In this paper, we present a numerical method to solve a linear fractional differential equations. This new investigation is based on ultraspherical integration matrix to approximate the highest order derivatives to the lower order derivatives. By this approximation the problem is reduced to a constrained optimization problem which can be solved by using the penalty quadratic interpolation method. Numerical examples are included to confirm the efficiency and accuracy of the proposed method.

Optimal Design of Coatings for Mirrors of Gravitational Wave Detectors: Analytic Turbo Solution via Herpin Equivalent Layers

In this paper, an analytical solution to the problem of optimal dielectric coating design of mirrors for gravitational wave detectors is found. The technique used to solve this problem is based on Herpin’s equivalent layers, which provide a simple, constructive, and analytical solution. The performance of the Herpin-type design exceeds that of the periodic design and is almost equal to the performance of the numerical, non-constructive optimized design obtained by brute force. Note that the existence of explicit analytic constructive solutions of a constrained optimization problem is not guaranteed in general, when such a solution is found, we speak of turbo optimal solutions.

Perceptual hashing method for video content authentication with maximized robustness

Perceptual video hashing represents video perceptual content by compact hash. The binary hash is sensitive to content distortion manipulations, but robust to perceptual content preserving operations. Currently, boundary between sensitivity and robustness is often ambiguous and it is decided by an empirically defined threshold. This may result in large false positive rates when received video is to be judged similar or dissimilar in some circumstances, e.g., video content authentication. In this paper, we propose a novel perceptual hashing method for video content authentication based on maximized robustness. The developed idea of maximized robustness means that robustness is maximized on condition that security requirement of hash is first met. We formulate the video hashing as a constrained optimization problem, in which coefficients of features offset and robustness are to be learned. Then we adopt a stochastic optimization method to solve the optimization. Experimental results show that the proposed hashing is quite suitable for video content authentication in terms of security and robustness.

A New Sequential Optimality Condition of Cardinality-Constrained Optimization Problem and Application

In this paper, we consider the cardinality-constrained optimization problem and propose a new sequential optimality condition for the continuous relaxation reformulation which is popular recently. It is stronger than the existing results and is still a first-order necessity condition for the cardinality constraint problem without any additional assumptions. Meanwhile, we provide a problem-tailored weaker constraint qualification, which can guarantee that new sequential conditions are Mordukhovich-type stationary points. On the other hand, we improve the theoretical results of the augmented Lagrangian algorithm. Under the same condition as the existing results, we prove that any feasible accumulation point of the iterative sequence generated by the algorithm satisfies the new sequence optimality condition. Furthermore, the algorithm can converge to the Mordukhovich-type (essentially strong) stationary point if the problem-tailored constraint qualification is satisfied.

A constrained optimal hear-through filter design approach for earphones

The sound from environment will be altered after it transmits through headphones to the ear canal. A hear-though filter can be designed and implemented in the headphones to create a more natural hearing experience, i.e., offer a transparent mode for headphones. The design of hear-through filter is also required in some other applications, e.g., augmented reality audio. In this paper, a constrained hear-through filter design approach is proposed. It is firstly shown that the hear-through filter design problem can be formulated in a similar form to active noise control filter design in the frequency domain. One advantage of this design approach is that multiple practical constraints can be applied conveniently by formulating a constrained optimization problem. Then the constrained optimization problem for hear-through filter design is reformulated as cone programming problem which can be solved efficiently. The proposed design approach can also specify the desired delay of reproduced sound. The designed filter can be directly implemented in an active noise control system in the headphone such that the requirement for extra electronic components can be minimal.

Energy-Efficient Cognitive Radio Sensor Networks: Parametric and Convex Transformations

Designing energy-efficient cognitive radio sensor networks is important to intelligently use battery energy and to maximize the sensor network life. In this paper, the problem of determining the power allocation that maximizes the energy-efficiency of cognitive radio-based wireless sensor networks is formed as a constrained optimization problem, where the objective function is the ratio of network throughput and the network power. The proposed constrained optimization problem belongs to a class of nonlinear fractional programming problems. Charnes-Cooper Transformation is used to transform the nonlinear fractional problem into an equivalent concave optimization problem. The structure of the power allocation policy for the transformed concave problem is found to be of a water-filling type. The problem is also transformed into a parametric form for which a ε-optimal iterative solution exists. The convergence of the iterative algorithms is proven, and numerical solutions are presented. The iterative solutions are compared with the optimal solution obtained from the transformed concave problem, and the effects of different system parameters (interference threshold level, the number of primary users and secondary sensor nodes) on the performance of the proposed algorithms are investigated.

Energy-Efficient Cognitive Radio Sensor Networks: Parametric and Convex Transformations

Designing energy-efficient cognitive radio sensor networks is important to intelligently use battery energy and to maximize the sensor network life. In this paper, the problem of determining the power allocation that maximizes the energy-efficiency of cognitive radio-based wireless sensor networks is formed as a constrained optimization problem, where the objective function is the ratio of network throughput and the network power. The proposed constrained optimization problem belongs to a class of nonlinear fractional programming problems. Charnes-Cooper Transformation is used to transform the nonlinear fractional problem into an equivalent concave optimization problem. The structure of the power allocation policy for the transformed concave problem is found to be of a water-filling type. The problem is also transformed into a parametric form for which a ε-optimal iterative solution exists. The convergence of the iterative algorithms is proven, and numerical solutions are presented. The iterative solutions are compared with the optimal solution obtained from the transformed concave problem, and the effects of different system parameters (interference threshold level, the number of primary users and secondary sensor nodes) on the performance of the proposed algorithms are investigated.