New technique for solving univariate global optimization

summary:In this paper, a new global optimization method is proposed for an optimization problem with twice differentiable objective function a single variable with box constraint. The method employs a difference of linear interpolant of the objective and a concave function, where the former is a continuous piecewise convex quadratic function underestimator. The main objectives of this research are to determine the value of the lower bound that does not need an iterative local optimizer. The proposed method is proven to have a finite convergence to locate the global optimum point. The numerical experiments indicate that the proposed method competes with another covering methods

PIECEWISE QUADRATIC BOUNDING FUNCTIONS FOR FINDING REAL ROOTS OF POLYNOMIALS

In this paper, our main interest is to create/ construct a new useful and outstanding algorithm to obtain roots of the real polynomial represented by f(x) = c(0) +c(1)x+ ... + c(i)x(i) + ... + c(n)(x)n where coefficients of the polynomials are real numbers and x is a real number in the closed interval of R. Also, our results are supported by numerical examples. Then, a new algorithm is compared with the others (writer classical methods) and this algorithm is more useful than others.WOS:0005948444000052-s2.0-8510123999