Concept
A non-convex function is a type of function where the line segment between any two points on the graph may not lie entirely above or on the graph, leading to multiple local minima and maxima. This characteristic makes optimization problems involving non-convex functions more challenging due to the possibility of getting trapped in local optima instead of finding the global optimum.
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Concept
A global optimum is the best possible solution or outcome in a mathematical model or optimization problem, considering all possible solutions. It contrasts with a local optimum, which is the best solution within a neighboring set of candidate solutions but not necessarily the best overall.
Concept
A global maximum is the highest point over the entire domain of a function, representing the largest value the function can achieve. It is crucial in optimization problems where the goal is to find the most optimal solution among all possible solutions.
Concept
A local optimum is a solution that is better than neighboring solutions but not necessarily the best overall solution in the entire search space. It is crucial in optimization problems where algorithms may settle for local optima rather than finding the global optimum, especially in complex or non-convex landscapes.
Concept
A local minimum is a point in a function where the function value is lower than at any nearby points, but not necessarily the lowest overall. It is crucial in optimization problems, where finding such points can help in understanding the behavior of the function and in solving real-world problems by identifying optimal solutions within a given region.
Convex optimization deals with problems where the objective function and feasible set are convex, ensuring any local minimum is a global minimum, making them easier to solve. Non-Convex optimization lacks these properties, often leading to multiple local minima and a more complex solution landscape, requiring advanced techniques for effective resolution.
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