admissible function

简明释义

1. 容许函数; 2. 可取函数;

英英释义

例句

1.In optimization problems, an admissible function is one that satisfies all the constraints of the problem.

在优化问题中，可接受函数是指满足所有约束条件的函数。

2.When defining a cost function, it is crucial to ensure that it is an admissible function to guarantee optimality.

在定义成本函数时，确保它是一个可接受函数至关重要，以保证最优性。

3.In game theory, an admissible function can help to evaluate potential strategies effectively.

在博弈论中，可接受函数可以有效地评估潜在策略。

4.The algorithm only accepts solutions that are based on an admissible function for pathfinding.

该算法仅接受基于可接受函数的路径寻找解决方案。

5.To prove convergence, we need to show that our iterative method uses an admissible function.

为了证明收敛性，我们需要展示我们的迭代方法使用了一个可接受函数。

作文

In the field of mathematics and statistics, the concept of an admissible function plays a crucial role in various applications, particularly in optimization problems and decision-making processes. An admissible function refers to a function that satisfies certain conditions or constraints that are deemed acceptable within a given context. Understanding the properties and implications of admissible functions can greatly enhance our ability to solve complex problems effectively.To illustrate the importance of admissible functions, let us consider a simple example in optimization. Imagine we are tasked with minimizing a cost function subject to specific constraints. The cost function represents the total expense incurred in a particular operation, while the constraints may include resource limitations, regulatory requirements, or physical boundaries. In this scenario, an admissible function would be one that adheres to these constraints while still allowing for the minimization of costs.The concept of admissibility is not limited to optimization alone; it also extends to statistical estimation. In statistics, an estimator is said to be admissible if there is no other estimator that performs better in terms of a specific loss function across all possible parameter values. This means that an admissible function provides a balance between bias and variance, leading to a more reliable estimation process. For instance, when estimating the mean of a population, using the sample mean as an estimator is often considered admissible because it minimizes the expected squared error compared to other potential estimators.Furthermore, the notion of admissible functions can be found in various fields such as economics, engineering, and computer science. For example, in economics, utility functions that represent consumer preferences must be admissible to ensure they reflect rational behavior. Similarly, in engineering, design functions must satisfy safety and performance criteria to be considered admissible for practical applications.Understanding admissible functions also involves recognizing their limitations. While they provide a framework for acceptable solutions, relying solely on admissible functions may lead to suboptimal outcomes if the underlying assumptions are not met. Therefore, it is essential to critically evaluate the context in which these functions are applied and to remain open to alternative approaches that may yield better results.In conclusion, the concept of an admissible function serves as a fundamental building block in various disciplines, guiding researchers and practitioners in their quest for optimal solutions. By adhering to the constraints and conditions that define admissible functions, we can enhance our decision-making processes and improve the quality of our outcomes. As we continue to explore the intricacies of mathematics and its applications, the understanding of admissible functions will undoubtedly remain a vital area of study, contributing to advancements in knowledge and practice across multiple domains.

在数学和统计学领域，可接受函数的概念在各种应用中发挥着至关重要的作用，特别是在优化问题和决策过程中。可接受函数指的是在特定上下文中被认为可以接受的函数，它满足某些条件或约束。理解可接受函数的性质和含义可以极大地增强我们有效解决复杂问题的能力。为了说明可接受函数的重要性，让我们考虑一个简单的优化示例。假设我们需要在特定约束条件下最小化一个成本函数。成本函数表示在特定操作中产生的总费用，而约束可能包括资源限制、法规要求或物理边界。在这种情况下，可接受函数将是一个遵循这些约束的同时仍允许成本最小化的函数。可接受性的概念不仅限于优化；它还扩展到统计估计。在统计学中，如果没有其他估计量在特定损失函数下在所有可能的参数值中表现更好，则该估计量被称为可接受。这意味着可接受函数在偏差和方差之间提供了平衡，从而导致更可靠的估计过程。例如，当估计一个总体的均值时，使用样本均值作为估计量通常被认为是可接受的，因为它最小化了相对于其他潜在估计量的期望平方误差。此外，可接受函数的概念可以在经济学、工程学和计算机科学等多个领域找到。例如，在经济学中，表示消费者偏好的效用函数必须是可接受的，以确保它们反映理性行为。同样，在工程学中，设计函数必须满足安全性和性能标准，才能被视为适用于实际应用的可接受。理解可接受函数还涉及认识到它们的局限性。虽然它们为可接受解决方案提供了框架，但如果仅依赖于可接受函数，可能会导致次优结果，因为基础假设未得到满足。因此，批判性地评估这些函数应用的上下文，并保持对可能产生更好结果的替代方法的开放态度是至关重要的。总之，可接受函数的概念在各个学科中作为基本构建块，为研究人员和从业者在追求最佳解决方案的过程中提供指导。通过遵循定义可接受函数的约束和条件，我们可以增强我们的决策过程，提高结果的质量。随着我们继续探索数学及其应用的复杂性，对可接受函数的理解无疑将仍然是一个重要的研究领域，为多个领域的知识和实践进步做出贡献。