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Many constrained optimization algorithms can be adapted to the unconstrained case, often via the use of a penalty method. However, search steps taken by the unconstrained method may be unacceptable for the constrained problem, leading to a lack of convergence. This is referred to as the Maratos effect. [3]
A penalty method replaces a constrained optimization problem by a series of unconstrained problems whose solutions ideally converge to the solution of the original constrained problem. The unconstrained problems are formed by adding a term, called a penalty function, to the objective function that consists of a penalty parameter multiplied by a ...
Query optimization is a feature of many relational database management systems and other databases such as NoSQL and graph databases. The query optimizer attempts to determine the most efficient way to execute a given query by considering the possible query plans .
When the objective function is differentiable, sub-gradient methods for unconstrained problems use the same search direction as the method of steepest descent. Subgradient methods are slower than Newton's method when applied to minimize twice continuously differentiable convex functions.
The conjugate gradient method can also be used to solve unconstrained optimization problems such as energy minimization. It is commonly attributed to Magnus Hestenes and Eduard Stiefel , [ 1 ] [ 2 ] who programmed it on the Z4 , [ 3 ] and extensively researched it.
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. [ 1 ] [ 2 ] It is generally divided into two subfields: discrete optimization and continuous optimization .
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.
The optimization problem is to minimize (), where is a vector in , and is a differentiable scalar function. There are no constraints on the values that x {\displaystyle \mathbf {x} } can take. The algorithm begins at an initial estimate x 0 {\displaystyle \mathbf {x} _{0}} for the optimal value and proceeds iteratively to get a better estimate ...