This paper presents computationally eecient algorithms for function approximation with hinging hyper-planes. Approximant units are added one at a time using the method of tting the residual. To t an individual unit we have to solve a sequence of Quadratic Programming problems, an approach which has proven to ooer signiicant advantages over derivative-based search algorithms. Empirical results o...

Newton’s method for solving variational inequalities is known to be locally quadratically convergent. By incorporating a line search strategy for the regularized gap function, Taji et al. (Mathematical Programming, 1993) have proposed a modification of a Newton’s method which is globally convergent and whose rate of convergence is quadratic. But the quadratic convergence has been shown only und...

In this work, we consider block-Jacobi methods with Newton steps in each subspace search and prove their local quadratic convergence to a local minimum with non-degenerate Hessian under some orthogonality assumptions on the search directions. Moreover, such a method is exemplified for non-unitary joint matrix diagonalization, where we present a block-Jacobi-type method on the oblique manifold w...

This paper analyzes a controllable discrete-time machine repair problem withL operating machines and two repairmen. The number of working servers can be adjusteddepending on the number of failed machines in the system one at a time at machine's failure orat service completion epochs. Analytical closed-form solutions of the stationary probabilities ofthe number of failed machines in the system a...

This paper offers a complete method to find the exact frequency, damping, amplitude, and phase of the exponential molds. A simulated signal is taken to fit the real one. When this simulated signal is equal to the real one, the parameters of the simulated signal are identical to the real values. This method includes three major steps, initial value setting, gradient method, and quadratic interpo...

Grover’s quantum algorithm promises a quadratic acceleration for any problem formulable as a search. For unstructured search problems, its implementation and performance are well understood. The curse of dimensionality and the intractibility of the general global optimisation problem require any identifiable structure or regularity to be incorporated into a solution method. This paper addresses...

A novel inexact smoothing method is presented for solving the second-order cone complementarity problems (SOCCP). Our method reformulates the SOCCP as an equivalent nonlinear system of equations by introducing a regularized Chen-Harker-Kanzow-Smale smoothing function. At each iteration, Newton’s method is adopted to solve the system of equations approximately, which saves computation work compa...

Stability analysis of fuzzy control systems using polynomial methods is proposed. First, a new approach is introduced to search for poles of a T-S fuzzy system in any mixed weighting case. Next, through the technique of the pole placement, a controller can be designed to achieve the desired response. Then, using the following methods, such as the Kharitonov polynomials, Edge Theorem, Routh stab...

We propose a sequential quadratic optimization method for solving nonlinear optimization problems with equality and inequality constraints. The novel feature of the algorithm is that, during each iteration, the primal-dual search direction is allowed to be an inexact solution of a given quadratic optimization subproblem. We present a set of generic, loose conditions that the search direction (i...

We propose a sequential quadratic optimization method for solving nonlinear constrained optimization problems. The novel feature of the algorithm is that, during each iteration, the primal-dual search direction is allowed to be an inexact solution of a given quadratic optimization subproblem. We present a set of generic, loose conditions that the search direction (i.e., inexact subproblem solut...