Algorithms of local optimization for problem solving involve checking function values for neighbors and moving to the best one until a stop condition is met.
The direction in local optimization is determined by the Hessian and works well when starting points are close to the extremum.
Using Cauchy's method for larger steps when far from the solution and switching to Newton's for points close to the solution is common.
Implementing tabu memory can prevent repetitive moves and facilitate intensive searching of solution neighborhoods.