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The optimization of portfolios is an example of multi-objective optimization in economics. Since the 1970s, economists have modeled dynamic decisions over time using control theory . [ 14 ] For example, dynamic search models are used to study labor-market behavior . [ 15 ]
Chance-constrained portfolio selection is an approach to portfolio selection under loss aversion.The formulation assumes that (i) investor's preferences are representable by the expected utility of final wealth, and that (ii) they require that the probability of their final wealth falling below a survival or safety level must to be acceptably low.
Nonlinear programming — the most general optimization problem in the usual framework Special cases of nonlinear programming: See Linear programming and Convex optimization above; Geometric programming — problems involving signomials or posynomials Signomial — similar to polynomials, but exponents need not be integers
For many problems in applied linear algebra, it is useful to adopt the perspective of a matrix as being a concatenation of column vectors. For example, when solving the linear system =, rather than understanding x as the product of with b, it is helpful to think of x as the vector of coefficients in the linear expansion of b in the basis formed by the columns of A.
Bayesian optimization of a function (black) with Gaussian processes (purple). Three acquisition functions (blue) are shown at the bottom. [19]Probabilistic numerics have also been studied for mathematical optimization, which consist of finding the minimum or maximum of some objective function given (possibly noisy or indirect) evaluations of that function at a set of points.
The adjoint state method is a numerical method for efficiently computing the gradient of a function or operator in a numerical optimization problem. [1] It has applications in geophysics, seismic imaging, photonics and more recently in neural networks. [2] The adjoint state space is chosen to simplify the physical interpretation of equation ...
Optimal control is an extension of the calculus of variations, and is a mathematical optimization method for deriving control policies. [6] The method is largely due to the work of Lev Pontryagin and Richard Bellman in the 1950s, after contributions to calculus of variations by Edward J. McShane . [ 7 ]
The constrained-optimization problem (COP) is a significant generalization of the classic constraint-satisfaction problem (CSP) model. [1] COP is a CSP that includes an objective function to be optimized. Many algorithms are used to handle the optimization part.