global minimum

简明释义

总体极小值

英英释义

例句

1.The algorithm successfully converged to the global minimum (全局最小值) after several iterations.

经过几次迭代，该算法成功收敛到global minimum（全局最小值）。

2.The global minimum (全局最小值) of the cost function indicates the most efficient resource allocation.

成本函数的global minimum（全局最小值）表示最有效的资源分配。

3.In optimization problems, finding the global minimum (全局最小值) is crucial for achieving the best solution.

在优化问题中，找到global minimum（全局最小值）对获得最佳解决方案至关重要。

4.In calculus, we often use derivatives to find the global minimum (全局最小值) of a function.

在微积分中，我们经常使用导数来寻找函数的global minimum（全局最小值）。

5.Many machine learning models aim to minimize the loss function to reach the global minimum (全局最小值).

许多机器学习模型旨在最小化损失函数，以达到global minimum（全局最小值）。

作文

In the field of optimization, the concept of global minimum plays a crucial role in finding the best possible solution to a problem. A global minimum refers to the lowest point in a given function over its entire domain. This means that no other point in the function has a lower value than the global minimum. Understanding this concept is essential for various applications, including mathematics, economics, and engineering. To illustrate the importance of a global minimum, consider a simple example involving a quadratic function. The graph of a quadratic function is a parabola, which can either open upwards or downwards. When the parabola opens upwards, it has a global minimum at its vertex. This point represents the least value that the function can attain. In practical terms, finding this global minimum allows us to determine the optimal solution for problems such as minimizing costs or maximizing efficiency.In contrast, if we only focus on local minima—points that are lower than their immediate neighbors—we may overlook the global minimum. Local minima can be misleading, especially in complex functions with multiple peaks and valleys. Therefore, it is imperative to employ strategies that ensure we are searching for the global minimum rather than settling for a local one. Techniques such as gradient descent are commonly used in optimization problems. This method involves iteratively moving towards the steepest descent until reaching a minimum. However, it is essential to note that gradient descent may sometimes converge to a local minimum instead of the global minimum if the starting point is not chosen carefully.Another significant application of the global minimum concept is in machine learning algorithms. Many machine learning models aim to minimize a loss function, which quantifies the difference between predicted and actual outcomes. The goal is to find the global minimum of this loss function, ensuring the model performs optimally on unseen data. If a model settles at a local minimum, it may lead to suboptimal performance, resulting in poor predictions.Moreover, the quest for a global minimum extends beyond mathematical functions. In real-world scenarios, businesses often seek to minimize expenses while maximizing profits. This requires analyzing various factors and constraints to identify the global minimum in operational costs. By doing so, companies can allocate resources more effectively and enhance their overall efficiency.In conclusion, grasping the concept of global minimum is vital for anyone involved in optimization tasks. Whether in mathematics, economics, or engineering, recognizing the significance of the global minimum ensures that we do not settle for suboptimal solutions. The pursuit of the global minimum drives innovation and improvement across various fields, ultimately leading to better decision-making and enhanced outcomes. As we continue to explore complex problems, the understanding of global minimum will remain a cornerstone of effective problem-solving strategies.

在优化领域，全局最小值的概念在寻找问题的最佳解决方案中起着至关重要的作用。全局最小值是指在给定函数的整个定义域内的最低点。这意味着在函数中没有其他点的值低于全局最小值。理解这一概念对于数学、经济学和工程等各种应用至关重要。为了说明全局最小值的重要性，考虑一个简单的二次函数示例。二次函数的图形是一个抛物线，可以向上或向下开口。当抛物线向上开口时，它在其顶点处具有全局最小值。这个点代表了函数可以达到的最小值。从实际角度看，找到这个全局最小值使我们能够确定诸如最小化成本或最大化效率等问题的最佳解决方案。相反，如果我们只关注局部最小值——比其邻近点低的点——我们可能会忽视全局最小值。局部最小值可能会产生误导，特别是在具有多个峰和谷的复杂函数中。因此，采用确保我们在寻找全局最小值而不是停留在局部最小值的策略是至关重要的。梯度下降等技术通常用于优化问题。该方法涉及迭代地朝着最陡下降的方向移动，直到达到最小值。然而，需要注意的是，如果起始点选择不当，梯度下降有时可能会收敛到局部最小值而不是全局最小值。全局最小值概念的另一个重要应用是在机器学习算法中。许多机器学习模型旨在最小化损失函数，该函数量化了预测结果与实际结果之间的差异。目标是找到此损失函数的全局最小值，确保模型在未见数据上的最佳表现。如果模型停留在局部最小值上，可能会导致次优性能，从而导致预测不准确。此外，追求全局最小值超越了数学函数。在现实世界中，企业通常寻求最小化支出，同时最大化利润。这需要分析各种因素和约束，以识别运营成本中的全局最小值。通过这样做，公司可以更有效地分配资源，提高整体效率。总之，掌握全局最小值的概念对于参与优化任务的任何人来说都是至关重要的。无论是在数学、经济学还是工程学中，认识到全局最小值的重要性确保我们不会满足于次优解决方案。对全局最小值的追求推动了各个领域的创新和改进，最终导致更好的决策和更好的结果。随着我们继续探索复杂问题，对全局最小值的理解将始终是有效问题解决策略的基石。