In the application of dynamic programming to mathematical optimization, Richard Bellman's Principle of Optimality is based on the idea that in order to solve a dynamic optimization problem from some starting period t to some ending period T, one implicitly has to solve subproblems starting from later dates s, where t < s < T.

This breaks a dynamic optimization problem into simpler subproblems, as Bellman's Principle of Optimality prescribes.

Still other methods in phonology ( e. g. Optimality Theory, which uses lattice graphs ) and morphology ( e. g. finite-state morphology, using finite-state transducers ) are common in the analysis of language as a graph.

Though this usually goes unacknowledged, Optimality Theory was strongly influenced by Natural Phonology ; both view phonology in terms of constraints on speakers and their production, though these constraints are formalized in very different ways.

Optimality theory assumes that these components are universal.

Optimality theory supposes that there are no language-specific restrictions on the input.

Optimality theory predicts that there cannot be more grammars than there are permutations of the ranking of CON.

The relationship between the " Discount Yield " and the Rate of Return on other financial assets is usually discussed in such economic and financial theories involving the inter-relation between various Market Prices, and the achievement of Pareto Optimality through the operations in the Capitalistic Price Mechanism ,< Ref Name =" Economics_Discount "/> as well as in the discussion of the " Efficient ( Financial ) Market Hypothesis ".< Ref Name =" Finance_Discount "/>< Ref Name =" Economics_Competition "> Competition from other firms who offer other Financial Assets that promise the Market Rate of Return forces the person who is asking for a delay in payment to offer a " Discount Yield " that is the same as the Market Rate of Return .</ ref > The person delaying the payment of the current Liability is essentially compensating the person to whom he / she owes money for the lost revenue that could be earned from an investment during the time period covered by the delay in payment.

Optimality theory is usually considered a development of generative grammar, which shares its focus on the investigation of universal principles, linguistic typology and language acquisition.

* G. Bienvenu and L. Kopp, “ Optimality of high resolution array processing using the eigensystem approach ”, IEEE Transactions on Acoustics, Speech and Signal Process, Vol.

* Maynard-Smith, J., 1987, « How to model evolution », in Dupré, J., ed., The Latest on the Best: Essays on Evolution and Optimality, Cambridge, MA, MIT Press, p. 119-131.

Optimality Theory is popularly used for phonology, the subfield to which it was originally applied, but has been extended to other areas of linguistics such as syntax and semantics.

Prince, along with Paul Smolensky, developed Optimality Theory, which was originally applied to phonology, but has been extended to other areas of linguistics such as syntax and semantics.

* Optimality, in economics ; see utility and economic efficiency

Autosegmental phonology later evolved into Feature Geometry, which became the standard theory of representation for the theories of the organization of phonology as different as Lexical Phonology and Optimality Theory.

In a course at the LSA summer institute in 1991, Alan Prince and Paul Smolensky developed Optimality Theory — an overall architecture for phonology according to which languages choose a pronunciation of a word that best satisfies a list of constraints which is ordered by importance: a lower-ranked constraint can be violated when the violation is necessary in order to obey a higher-ranked constraint.

Broadly speaking Government Phonology ( or its descendant, Strict-CV Phonology ) has a greater following in the United Kingdom, whereas Optimality Theory is predominant in North America.

* Mathur, Vijay K. " How Well Do We Know Pareto Optimality?

Satisficing and Optimality.

Optimality theory ( frequently abbreviated OT ) is a linguistic model proposing that the observed forms of language arise from the interaction between conflicting constraints.

Optimality theory was originally proposed by the linguists Alan Prince and Paul Smolensky in 1993, and later expanded by Prince and John J. McCarthy.

Optimality theory is often called a connectionist theory of language, because it has its roots in neural network research, though the relationship is now largely of historical interest.

The Principle of Optimality is used to derive the Bellman equation, which shows how the value of the problem starting from t is related to the value of the problem starting from s.

Optimality statements ( minimum, maximum, optimum, end design, destiny ), have no place in constructal theory.

** This assumption also set the stage for using techniques of constrained optimization.

* symbolic constrained and unconstrained global optimization

Illustration of the constrained optimization problem

Illustration of the constrained optimization problem

This constrained optimization problem is typically solved using the method of Lagrange multipliers.

The models that make up consumer theory are used to represent prospectively observable demand patterns for an individual buyer on the hypothesis of constrained optimization.

: This assumption also set the stage for using techniques of constrained optimization.

*" An elitist teaching-learning-based optimization algorithm for solving complex constrained optimization problems ".

More generally, the second-order conditions that are sufficient for a local minimum or maximum can be expressed in terms of the sequence of principal ( upper-leftmost ) minors ( determinants of sub-matrices ) of the Hessian ; these conditions are a special case of those given in the next section for bordered Hessians for constrained optimization — the case in which the number of constraints is zero.

A bordered Hessian is used for the second-derivative test in certain constrained optimization problems.

) Because it changes the constrained optimization problem associated with reliability-based optimization into an unconstrained optimization problem, it often leads to computationally more tractable problem formulations.

The primal-dual method's idea is easy to demonstrate for constrained nonlinear optimization.

In constrained optimization in economics, the shadow price is the instantaneous change per unit of the constraint in the objective value of the optimal solution of an optimization problem obtained by relaxing the constraint.

However, David Zuckerman showed in 1996 that every one of these 21 problems has a constrained optimization version that is impossible to approximate within any constant factor unless P

The expenditure function is the minimand of the constrained optimization problem characterized by the following Lagrangian:

When specialised to posets, it becomes a relatively familiar type of question on ' constrained optimization '.

Multilevel Coordinate Search ( MSC ) is an algorithm for bound constrained global optimization using function values only.