I was wondering what differences and relations are between search methods and optimization methods? Especially when solving an optimization problem? I emphasize the context of solving optimization problems, because I guess search methods are not just for solving optimization problems, but also non-optimization  problems?My confusion comes from the following facts:There are some optimization methods, named xxx search, such aslocal search, stochastic search, .... What does search mean actually? I wonder if there areoptimization methods that are not search?Also in this book Introduction to Stochastic Search andOptimization by Spall, I don't quite understand the differencebetween Search and Optimization in its title as well as in itscontent. Why needs to distinguish between Search andOptimization, if they mean the same? Or does Optimization meanstochastic optimization tasks/problems instead of optimizationmethods, as opposed to search means the methods to solve theoptimization tasks/problems?Also No free lunch in search and optimization distinguishessearch and optimization again.Thanks and regards!
Meaning of search methods and optimization methods
optimization
search = attempt to find a feasible point that satisfies all constraints (and for optimization a better point than found so far), generally using function values only.local search: improving a feasible point (or a distance to feasibility measure) by searching among neighboring points.stochastic search: searching using a nondeterministic criterion for choosing trial points. This is independent of whether an optimization criterion is given. In particular, in ''No free lunch in search and optimization'' search refers to search for feasibility, while optimization refers to search for optimality.In a general sense, for optimization problem, search and optimization are equivalent. However, they have connotations that make a difference in the usage of the term.optimization method = a method for solving an optimization problem, often (but not necessarily) using gradient (or subgradient or even Hessian) information.Being able to use gradients drastically increases the efficiency of optimization methods. One uses in this context (i.e., with gradients known) to the term search only in the combination ''line search'' which means searching for a better point along a chosen direction.