I. Introduction. The solutions of the quadratic equation ax2 + bx+c = 0, where a, b, and c are real numbers, are given in exact form by the quadratic formula. Moreover, if the roots are real and irrational, Newton's method or continued fractions may be used to approximate the solutions.

This work evaluates the performance of high-resolution quadratic time-frequency distributions (TFDs) including the ones obtained by the reassignment method, the optimal radially Gaussian kernel method, the t-f autoregressive moving-average spectral estimation method and the neural network-based method. The approaches are rigorously compared to each other using several objective measures. Experi...

In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust when applied to highly nonseparable or ill conditioned problems. We call the method Robust Coordinate Descent (RCD). At each iteratio...

This paper presents a hybrid approach called frequent pattern based search that combines data mining and optimization. The proposed method uses a data mining procedure to mine frequent patterns from a set of high-quality solutions collected from previous search, and the mined frequent patterns are then employed to build starting solutions that are improved by an optimization procedure. After pr...

This paper presents an algorithm for solving optimal power flow problem through the application of Differential Evolution (DE). The objective is to minimize the total fuel cost of thermal generating units having quadratic cost characteristics subjected to limits on generator real and reactive power outputs, bus voltages, transformer taps and power flow of transmission lines. The proposed method...

This paper focuses on the design of control Lyapunov function for control affine systems to guarantee the stability for the states of interest in a specified region. Without restrictive assumptions found in previous approaches, a min-max optimization problem is formulated to solve for a quadratic Lyapunov function. A derivative-free coordinate search method is employed to optimize a non-differe...

Maximum likelihood (ML) for phylogenetic inference from sequence data remains a method of choice, but has computational limitations. In particular, it cannot be applied for a global search through all potential trees when the number of taxa is large, and hence a heuristic restriction in the search space is required. In this paper, we derive a quadratic approximation, QAML, to the likelihood fun...

Sparse generalized eigenvalue problem arises in a number of standard and modern statistical learning models, including sparse principal component analysis, sparse Fisher discriminant analysis and sparse canonical correlation analysis. However, this problem is difficult to solve since it is NP-hard. In this paper, we consider a new decomposition method to tackle this problem. Specifically, we us...

This paper presents a method to encapsulate parameters of evolutionary algorithms and to create an abstraction that simplifies the control and the understanding of the internal behavior of the algorithm. A fuzzy model is used to learn the effects of parameters over the search process. Then, high-level strategies can be defined to modify parameters automatically in order to achieve a scheduled l...