Journal ArticleDOI
Globally minimizing polynomials without evaluating derivatives
TLDR
In this paper, a simple algorithm for globally minimizing a polynomial on a compact interval of the real line is proposed, which is based upon the idea of local approximation, is finitely convergent and reliable.Abstract:
A simple algorithm for globally minimizing a polynomial on a compact interval of the real line is proposed. The algorithm is based upon the idea of local polynomial approximation, is finitely convergent and reliable. Moreover, no derivatives of the polynomial are evaluated. Some examples of the numerical behavior of the algorithm are given.read more
Citations
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Journal ArticleDOI
A Branch-and-Reduce Approach to Global Optimization
TL;DR: Valid inequalities and range contraction techniques that can be used to reduce the size of the search space of global optimization problems are presented and incorporated within the branch-and-bound framework to result in a branch- and-reduce global optimization algorithm.
Journal ArticleDOI
A global optimization algorithm (GOP) for certain classes of nonconvex NLPs—I. Theory
TL;DR: Application of the theory and the GOP algorithm to various classes of optimization problems, as well as computational results of the approach are provided.
Book ChapterDOI
D.C. Optimization: Theory, Methods and Algorithms
TL;DR: This work presents a review of the theory, methods and algorithms for this class of global optimization problems which have been elaborated in recent years.
Journal ArticleDOI
A global optimization algorithm (GOP) for certain classes of nonconvex NLPs—II. Application of theory and test problems
V. Visweswaran,C.A. Floudast +1 more
TL;DR: In this paper, theoretical results are presented for several classes of mathematical programming problems that include: the general quadratic programming problem, and unconstrained and constrained optimization problems with polynomial terms in the objective function and/or constraints.
Journal ArticleDOI
New reformulation linearization/convexification relaxations for univariate and multivariate polynomial programming problems
TL;DR: Several new classes of constraints are introduced for both univariate and multivariate versions of this problem, including certain simple convex variable bounding types of restrictions that can be used to augment the basic (linear) RLT relaxation in order to yield tighter lower bounds.
References
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Book
Algorithms for Minimization Without Derivatives
TL;DR: In this paper, a monograph describes and analyzes some practical methods for finding approximate zeros and minima of functions, and some of these methods can be used to find approximate minima as well.
Journal ArticleDOI
On descent from local minima
A. A. Goldstein,J. F. Price +1 more
TL;DR: In this paper, a process with analytical criteria is described which sometimes finds smaller local minima in an algorithmic manner, under the assumption that a local minimum is known, and the process to be described sometimes finds the smaller local minimizers in an analytical manner.
Journal ArticleDOI
Bounds for an interval polynomial
TL;DR: The evaluation of the range of values of an interval polynomial over an interval is discussed and several algorithms are proposed and tested on numerical examples.
Book ChapterDOI
Finding the global minimum of a function of one variable using the method of constant signed higher order derivatives
TL;DR: In this paper, a method for obtaining a global minimizer of the problem: minimize f(x) s.t. L ≤ x ≤ U ≤ U is presented for continuous derivatives, where subintervals are found on which certain derivatives have constant sign.
Related Papers (5)
A global optimization algorithm (GOP) for certain classes of nonconvex NLPs—I. Theory
A global optimization algorithm (GOP) for certain classes of nonconvex NLPs—II. Application of theory and test problems
V. Visweswaran,C.A. Floudast +1 more