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The MM algorithm is an iterative optimization method which exploits the convexity of a function in order to find its maxima or minima. The MM stands for “Majorize-Minimization” or “Minorize-Maximization”, depending on whether the desired optimization is a minimization or a maximization.
Optimal stopping problems can be found in areas of statistics, economics, and mathematical finance (related to the pricing of American options). A key example of an optimal stopping problem is the secretary problem.
Using Lagrange multipliers, this problem can be converted into an unconstrained optimization problem: (,) = + . The two critical points occur at saddle points where x = 1 and x = −1 . In order to solve this problem with a numerical optimization technique, we must first transform this problem such that the critical points occur at local minima.
Given a system minimize subject to ,, the reduced cost vector can be computed as , where is the dual cost vector. It follows directly that for a minimization problem, any non- basic variables at their lower bounds with strictly negative reduced costs are eligible to enter that basis, while any basic variables must have a reduced cost that is ...
The result of fitting a set of data points with a quadratic function Conic fitting a set of points using least-squares approximation. In regression analysis, least squares is a parameter estimation method based on minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each ...
Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions.Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constraints on the variables.