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Multi-disciplinary design optimization (MDO) is a field of engineering that uses optimization methods to solve design problems incorporating a number of disciplines. It is also known as multidisciplinary system design optimization (MSDO), and Multidisciplinary Design Analysis and Optimization (MDAO).
In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear.
In calculus, Newton's method (also called Newton–Raphson) is an iterative method for finding the roots of a differentiable function F, which are solutions to the equation F (x) = 0. As such, Newton's method can be applied to the derivative f ′ of a twice-differentiable function f to find the roots of the derivative (solutions to f ′(x) = 0), also known as the critical points of f. These solutions may be minima, maxima, or saddle points; see section "Several variables" in Critical point (mathematics) and also section "Geometric interpretation" in this article. This is relevant in optimization, which aims to find (global) minima of the function f.
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Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization which may be considered a quasi-Newton method. SQP methods are used on mathematical problems for which the objective function and the constraints are twice continuously differentiable, but not necessarily convex.
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Naum Zuselevich Shor was a Soviet and Ukrainian mathematician specializing in optimization.
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Sequential linear-quadratic programming (SLQP) is an iterative method for nonlinear optimization problems where objective function and constraints are twice continuously differentiable. Similarly to sequential quadratic programming (SQP), SLQP proceeds by solving a sequence of optimization subproblems. The difference between the two approaches is that:
References
- ↑ ( Nocedal & Wright 2006 , p. 551)
- ↑ ( Bazaraa, Sherali & Shetty 1993 , p. 432)
- ↑ ( Palacios-Gomez, Lasdon & Enquist 1982 )
