An NLP problem where the objective and all constraints are convex functions can be solved efficiently to global optimality, up to very large size; interior point methods are normally very effective on the largest convex problems.
But if the objective or any constraints are non-convex , the problem may have multiple feasible regions and multiple locally optimal points within such regions. It can take time exponential in the number of variables and constraints to determine that a non-convex NLP problem is infeasible, that the objective function is unbounded, or that an optimal solution is the "global optimum" across all feasible regions.
Although functions can be non-smooth but convex or smooth but non-convex , you can expect much better performance with most Solvers if your problem functions are all smooth and convex.
There are a variety of methods for solving NLP problems, and no single method is best for all problems. NLP solvers generally exploit the smoothness of the problem functions by computing gradient values at various trial solutions, and moving in the direction of the negative gradient when minimizing; the positive gradient when maximizing.
They usually also exploit second derivative information to follow the curvature as well as the direction of the problem functions. Is it "not linear" or something different? Ask Question. Asked 8 years ago. Active 8 years ago. Viewed times. Does the nonlinearity mean nonlinear objective function? Community Bot 1. The real question then is, "What needs to be linear for the problem to be considered linear?
Moved the new question now here. Add a comment. Active Oldest Votes. Possibly II. None, in general. Eric Stucky Eric Stucky So did I change the nonlinear problem into a linear problem or just to totally different linear problem? If you had some compelling reason why any situation that could be modeled by the first could be equally well modeled by the second, then we would call them "the same".
But if the answers are the same, all you know is that the optimum for the two situations is identical; in particular a near-optimum solution for the two problems might look quite different even qualitatively. My teacher said that anyone in the course can ask questions in any place such as Math.
Stackexchange and even share answers so this is not cheating but open discussion so what is the pedagogy or the goal behind such questions? I think that's as simple as you can get for an answer. In a linear problem there is a constant of variation that is consistent with each data point.
Whereas in a non linear problem, the constant of variation changes from on data point to another. The first constant of variation changes from 3 to 5 to 7 as x increases. Graph this one and see how these non-linear problems differ. When the maximum power of all variables in a term added together in an equation is 1 it is linear. When you have an equation with maximum power added together in a term of the variables not equal to 1, it is non-linear.
A linear problem is any problem which is solved by setting up only linear equations or linear systems of equations to solve.
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