Feedback Optimality Condition for Nonconvex Discrete Linear-Quadratic Optimal Control Problem

The paper analyzed a non-convex linear-quadratic optimization problem in a discrete dynamic system. We obtained necessary optimality condition with feedback controls which allow a descent of the functional cost. Such controls are generated by the quadratic majorant of the cost. In contrast to the discrete maximum principle, this condition does not require any convexity properties of the problem.

Feature Level Fusion Algorithm for Iris and Face

Some Bi-modal or multimodal recognition systems do not contain rich information needed for identification because information supplied to the biometric classifier are consolidated oncethe conclusions of the matching algorithm have been acquired. Feature based Fusion algorithm has the distinction of having richer information due to the integration of the extracted information before the application of the classifiers. Support Vector Machine over time has shown its unbeatable classification of the biometrics characteristics over other supervised learning classifiers due to its ability to minimize the structural risk simultaneously with bound on the margin complexity and by being solved using a quadratic optimization problem. Neural Network in contrast is a non-parametric estimator which is robust to errors in the training data used for classification and regression. Therefore in this research, algorithms for feature extraction of iris and face for recognition is designed; a recognition system using SVM and Multilayer Perceptron (MLP) is also designed based on the extracted features and the designed model is implemented using MATLAB

Extending the Scope of Robust Quadratic Optimization

We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. Our results provide extensions to known results from the literature. We also consider hard quadratic constraints: those that are convex in uncertain matrix-valued parameters. For the robust counterpart of such constraints, we derive inner and outer tractable approximations. As an application, we show how to construct a natural uncertainty set based on a statistical confidence set around a sample mean vector and covariance matrix and use this to provide a tractable reformulation of the robust counterpart of an uncertain portfolio optimization problem. We also apply the results of this paper to norm approximation problems. Summary of Contribution: This paper develops new theoretical results and algorithms that extend the scope of a robust quadratic optimization problem. More specifically, we derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We also consider hard quadratic constraints: those that are convex in uncertain matrix-valued parameters. For the robust counterpart of such constraints, we derive inner and outer tractable approximations.

The sufficient condition to find an exact dual bound in a separable quadratic optimization problem

The paper considers nonconvex separable quadratic optimization problems subject to inequality constraints. A sufficient condition is given for finding the value and the point of the global extremum of a problem of this type by calculating the Lagrange dual bound. The peculiarity of this condition is that it is easily verified and requires from the Hessian matrix of the Lagrange function only that its region of positive definiteness is not empty. The result obtained for the dual bound also holds for the bound obtained using SDP relaxation.

Improved Single Inertial-Sensor-Based Attitude Estimation during Walking Using Velocity-Aided Observation

This paper presents a Kalman filter-based attitude estimation algorithm using a single body-mounted inertial sensor consisting of a triaxial accelerometer and triaxial gyroscope. The proposed algorithm has been developed for attitude estimation during dynamic conditions such as walking and running. Based on the repetitive properties of the velocity signal of human gait during walking, a novel velocity-aided observation is used as a measurement update for the filter. The performance has been evaluated in comparison to two standard Kalman filters with different measurement update methods and a smoother algorithm which is formulated in the form of a quadratic optimization problem. Whereas two standard Kalman filters give maximum 5 degrees in both pitch and roll error for short walking case, their performance gradually decrease with longer walking distance. The proposed algorithm shows the error of about 3 degrees in 15 m walking case, and indicate the robustness of the method with the same performance in 75 m trials. As far as the accuracy of the estimation is concerned, the proposed method achieves advantageous results due to its periodic error correction capability in both short and long walking cases at varying speeds. In addition, in terms of practicality and stability, with simple parameter settings and without the need of all-time data, the algorithm can achieve smoothing-algorithm-performance level with lower computational resources.

Characterization of Robust Solution Quadratically Constrained Quadratic Optimization Problem Subjected to Data Uncertainty

Robust Optimization (RO) arises in two stages of optimization, first level for maximizing over the uncertain data and second level for minimizing over the feasible set. It is the most suitable mathematical optimization procedure to solve real-life problem models. In the present work, we characterize robust solutions for both homogeneous and non-homogeneous quadratically constrained quadratic optimization problem where constraint function and cost function are uncertain. Moreover, we discuss about optimistic dual and strong robust duality of the considered uncertain quadratic optimization problem. Finally, we complete this work with an example to illustrate our solution method. Mathematics Subject Classification: (2010) 90C20 - 90C26 - 90C46-90C47 Keywords: Robust Optimization, Data Uncertainty, Quadratic Optimization Strong Duality, Robust Solution, DPJ-Convex.

Solving Fractional Differential Equations by Using Triangle Neural Network

In this paper, numerical methods for solving fractional differential equations by using a triangle neural network are proposed. The fractional derivative is considered Caputo type. The fractional derivative of the triangle neural network is analyzed first. Then, based on the technique of minimizing the loss function of the neural network, the proposed numerical methods reduce the fractional differential equation into a gradient descent problem or the quadratic optimization problem. By using the gradient descent process or the quadratic optimization process, the numerical solution to the FDEs can be obtained. The efficiency and accuracy of the presented methods are shown by some numerical examples. Numerical tests show that this approach is easy to implement and accurate when applied to many types of FDEs.

Exact Facetial Odd-Cycle Separation for Maximum Cut and Binary Quadratic Optimization

The exact solution of the NP-hard (nondeterministic polynomial-time hard) maximum cut problem is important in many applications across, for example, physics, chemistry, neuroscience, and circuit layout—which is also due to its equivalence to the unconstrained binary quadratic optimization problem. Leading solution methods are based on linear or semidefinite programming and require the separation of the so-called odd-cycle inequalities. In their groundbreaking research, F. Barahona and A. R. Mahjoub have given an informal description of a polynomial-time algorithm for this problem. As pointed out recently, however, additional effort is necessary to guarantee that the inequalities obtained correspond to facets of the cut polytope. In this paper, we shed more light on a so enhanced separation procedure and investigate experimentally how it performs in comparison with an ideal setting where one could even employ the sparsest, most violated, or geometrically most promising facet-defining odd-cycle inequalities. Summary of Contribution: This paper aims at a better capability to solve binary quadratic optimization or maximum cut problems and their various applications using integer programming techniques. To this end, the paper describes enhancements to a well-known algorithm for the central separation problem arising in this context; it is demonstrated experimentally that these enhancements are worthwhile from a computational point of view. The linear relaxations of the aforementioned problems are typically solved using fewer iterations and cutting planes than with a nonenhanced approach. It is also shown that the enhanced procedure is only slightly inferior to an ideal, enumerative, and, in practice, intractable global cutting-plane selection.

Numerical Simulation of Dynamic Fluid-Structure Interaction with Elastic Structure–Rigid Obstacle Contact

An implicit scheme by partitioned procedures is proposed to solve a dynamic fluid–structure interaction problem in the case when the structure displacements are limited by a rigid obstacle. For the fluid equations (Sokes or Navier–Stokes), the fictitious domain method with penalization was used. The equality of the fluid and structure velocities at the interface was obtained using the penalization technique. The surface forces at the fluid–structure interface were computed using the fluid solution in the structure domain. A quadratic optimization problem with linear inequalities constraints was solved to obtain the structure displacements. Numerical results are presented.