What are the problems of mixed integer nonlinear programming?

What are the problems of mixed integer nonlinear programming?

Mixed-integer nonlinear programming (MINLP) problems combine the combinatorial difficulty of optimizing over discrete variable sets with the challenges of handling nonlinear func- tions.

Are there undecidable nonconvex integer optimization problems?

Worse, nonconvex integer optimization problems are in general undecidable (Jeroslow,1973). Jeroslow provides an example of a quadratically constrained integer program and shows that no computing device exists that can compute the optimum for all problems in this class.

Why are nonconvex MINLPs a challenge for optimization?

Nonconvex MINLPs pose additional challenges, because they contain nonconvex functions in the objective or the constraints; hence even when the integer variables are relaxed to be con- tinuous, the feasible region is generally nonconvex, resulting in many local minima.

Which is the most efficient method for convex MINLP?

The most efficient class of methods for convex MINLP are hybrid methods that combine the strengths of both classes of classical techniques.

How is the speedup of mixed integer linear programming?

However, the results also show the difficulty of taking full advantage of multiple threads, and on average the speedups remain modest. For an individual problem the speedup may be significantly larger, and there are instances where the solution time is reduced by more than 75 %.

Which is NP hard combinatorial problem for integer optimization?

Problem (1.1) is an NP-hard combinatorial problem, because it includes MILP (Kannan and Monma,1978), and its solution typically requires searching enormous search trees; see Figure1. Worse, nonconvex integer optimization problems are in general undecidable (Jeroslow,1973).

When is a problem called a nonlinear problem?

The problem is called a nonlinear programming problem (NLP) if the objective function is nonlinear and/or thefeasible region is determined by nonlinear constraints.

Is it hard to do nonlinear polynomial optimization?

Even in the pure continuous case, nonlinear optimization is known to be hard. Theorem 1. Pure continuous polynomial optimization over polytopes (n. 2 = 0) in varying dimension is NP-hard. Moreover, there does not exist a fully polynomial time approximation scheme (FPTAS) (unless P =NP).