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A Combination Technique for Optimal Control Problems Constrained by Random PDEs
Related concepts (37)
Cutting stock problem
In operations research, the cutting-stock problem is the problem of cutting standard-sized pieces of stock material, such as paper rolls or sheet metal, into pieces of specified sizes while minimizing material wasted. It is an optimization problem in mathematics that arises from applications in industry. In terms of computational complexity, the problem is an NP-hard problem reducible to the knapsack problem. The problem can be formulated as an integer linear programming problem.
Asymptotic analysis
In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function f (n) as n becomes very large. If f(n) = n2 + 3n, then as n becomes very large, the term 3n becomes insignificant compared to n2. The function f(n) is said to be "asymptotically equivalent to n2, as n → ∞". This is often written symbolically as f (n) ~ n2, which is read as "f(n) is asymptotic to n2".
Technical analysis
In finance, technical analysis is an analysis methodology for analysing and forecasting the direction of prices through the study of past market data, primarily price and volume. As a type of active management, it stands in contradiction to much of modern portfolio theory. The efficacy of technical analysis is disputed by the efficient-market hypothesis, which states that stock market prices are essentially unpredictable, and research on whether technical analysis offers any benefit has produced mixed results.
Axiom of regularity
In mathematics, the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set A contains an element that is disjoint from A. In first-order logic, the axiom reads: The axiom of regularity together with the axiom of pairing implies that no set is an element of itself, and that there is no infinite sequence (an) such that ai+1 is an element of ai for all i.
Spaces of test functions and distributions
In mathematical analysis, the spaces of test functions and distributions are topological vector spaces (TVSs) that are used in the definition and application of distributions. Test functions are usually infinitely differentiable complex-valued (or sometimes real-valued) functions on a non-empty open subset that have compact support. The space of all test functions, denoted by is endowed with a certain topology, called the , that makes into a complete Hausdorff locally convex TVS.
Fundamental analysis
Fundamental analysis, in accounting and finance, is the analysis of a business's financial statements (usually to analyze the business's assets, liabilities, and earnings); health; and competitors and markets. It also considers the overall state of the economy and factors including interest rates, production, earnings, employment, GDP, housing, manufacturing and management. There are two basic approaches that can be used: bottom up analysis and top down analysis.
Epsilon-induction
In set theory, -induction, also called epsilon-induction or set-induction, is a principle that can be used to prove that all sets satisfy a given property. Considered as an axiomatic principle, it is called the axiom schema of set induction. The principle implies transfinite induction and recursion. It may also be studied in a general context of induction on well-founded relations. The schema is for any given property of sets and states that, if for every set , the truth of follows from the truth of for all elements of , then this property holds for all sets.