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Local and global maxima and minima for cos(3πx)/x, 0.1≤ x ≤1.1. In mathematical analysis, the maximum and minimum [a] of a function are, respectively, the greatest and least value taken by the function.
This represents the value (or values) of the argument x in the interval (−∞,−1] that minimizes (or minimize) the objective function x 2 + 1 (the actual minimum value of that function is not what the problem asks for).
The duality gap is the difference between the values of any primal solutions and any dual solutions. If is the optimal dual value and is the optimal primal value, then the duality gap is equal to . This value is always greater than or equal to 0 (for minimization problems).
In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables.
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.
Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to ...
Unlike classical utilitarianism, in which right actions are defined as those that maximize pleasure and minimize pain, preference utilitarianism entails promoting actions that fulfil the interests (i.e., preferences) of those beings involved. [2]
Leonard J. Savage argued that using non-Bayesian methods such as minimax, the loss function should be based on the idea of regret, i.e., the loss associated with a decision should be the difference between the consequences of the best decision that could have been made under circumstances will be known and the decision that was in fact taken before they were known.