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22 votes

What are good reference books for introduction to operations research?

For books with a focus on industrial applications, see this other question of this forum As textbooks, I would recommend to have a look at: General Intro to OR: W. Winston. Operations Research: ...
12 votes
Accepted

What global MINLP solvers support trigonometric functions?

SCIP does not currently support any trigonometric functions as of this post from May 2018. COUENNE appears to handle $\sin$ and $\cos$ expressions. ANTIGONE appears to not support any trigonometric ...
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11 votes
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Do the KKT conditions hold for mixed integer nonlinear problems?

No, the KKT conditions aren't applicable to mixed-integer programming problems with integer variables. The theory behind the KKT conditions depends on the objective and constraint functions being ...
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7 votes

What global MINLP solvers support trigonometric functions?

Here is an option for MATLAB users which is not mentioned in any other answers. YALMIP's BMIBNB iI a global branch and bound solver https://yalmip.github.io/solver/bmibnb/. It is used in combination ...
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6 votes

Understanding why this MINLP formulation is infeasible

There is a systematic way of finding the infeasibility of your problem. You would like to find the Irreducibly Inconsistent System (IIS) of your model. This technology is available in CPLEX and Gurobi ...
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  • 1,045
6 votes

What global MINLP solvers support trigonometric functions?

From the presentation given by Vigerske, S. (2015), it is noted that the solvers Couenne by P. Belotti and LindoAPI by Y. Lin and L. Schrage can handle trigonometric expressions. Both are ...
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  • 5,185
5 votes

What global MINLP solvers support trigonometric functions?

Octeract Engine (the solver I develop), is a deterministic global MINLP solver that supports all trigonometric functions (including hyperbolic functions).
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5 votes

Integer Decision Variables Always Forced to Zero in Minimization Problem (MINLP)

You can try adding a constraint forcing one of the affected variable to be nonzero. If the model becomes infeasible, you can try to find the conflicting constraints. If the model stays feasible, this ...
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  • 1,102
5 votes

Formulating a MINLP for CPLEX in PYOMO

As mentioned in the comments, CPLEX cannot handle MINLP problems which are not Mixed-Integer Second-order cones (MISOCP) and Mixed-integer quadratic or quadratically constrained programs (MIQP and ...
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  • 1,045
5 votes
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Solving a non-linear non-convex mixed-integer program

If you have the mathematical formulas for your problem (i.e., it's not black box), you can use a local MINLP solver, such as BONMIN, KNITRO, or MINOTAUR, or a deterministic global optimisation solver ...
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5 votes

MINLP involving integrals, sparse matrices and CDF of random variables. Best environment?

I suggest you have a look at LocalSolver to solve your problem. It is free for basic research and teaching. Contrarily to its name suggests, LocalSolver is a global optimization solver. It handles ...
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  • 2,649
4 votes

MINLP involving integrals, sparse matrices and CDF of random variables. Best environment?

So it seems your strategy (enumerative search on the integer variables) works well, and the issue is solving pure NLP problems. The choice of programming/modeling language you use is dependent on what ...
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  • 2,110
4 votes
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Global Optimization when the exponential function is involved

This is a non-convex global optimisation problem. The state-of-the-art way to solve this is to use a factorable relaxation. A key insight here is that $e^{-\alpha X}$ is convex (since your $\alpha$ is ...
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4 votes

Global Optimization when the exponential function is involved

Assuming the continuous relaxation is convex you can most likely use conic optimization with the exponential cone. The Mosek modelling cookbook has the details. Unsurprisingly Mosek can solve the ...
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  • 2,451
4 votes
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What is the technique of branch-and-bound used in Knitro to solve MINLP?

Knitro offers two variations of branch-and-bound for mixed-integer nonlinear programs. The first (and default method) is a standard branch-and-bound method that solves a continuous nonlinear ...
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  • 56
3 votes

Integer Decision Variables Always Forced to Zero in Minimization Problem (MINLP)

I only skimmed your model so others may be better able to point to the error directly, but here are some reasons this may occur: Constraints: as you mention, perhaps they're set so that it's not ...
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  • 1,307
3 votes

What is the technique of branch-and-bound used in Knitro to solve MINLP?

As KNITRO's manual says, it's vanilla branch-and-bound: the integer variables are relaxed to continuous, and solving that relaxed problem provides the bound for branch and bound. Since in this case ...
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3 votes
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How to define hybrid variables without using additional binary variables?

An alternative approach to binary variables or semicontinuous variables is the following cubic polynomial inequality: $$x(x-L_B)(U_B-x)\ge 0$$ Because $x \ge 0$, this constraint enforces $$(x = 0) \...
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  • 22.2k
2 votes

Global Optimization when the exponential function is involved

You may find a partial answer to your question in the following article (forthcoming in OR) by JP Vielma and J Huchette https://arxiv.org/abs/1708.00050 In that paper, the authors consider the problem ...
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2 votes

How to define a stationary point of the MINLP problem?

Welcome to OR Stack Exchange. Your question is not clear. You are interested in special points in discrete optimization spaces. But you describe a mixed-variable problem involving both continuous ...
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  • 2,649
1 vote
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Large MINLP problem, searching for solver, tried BARON, ANTIGONE, DICOPT

If a deterministic global optimisation solver (such as Baron) reports a local solution, that solution is reliable. If the solver is terminated prematurely, the global solver will return the best ...
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1 vote

MINLP Solution same as Global Optimum?

Technically, your statement is correct, but nowadays it depends on who you're talking to. Historically, to $\min f(x) s.t. ...$ means exactly what we see: to find the minimal value. Not some value ...
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1 vote

MINLP Solution same as Global Optimum?

This question is a matter of semantics. If by "solution", you mean the global optimum, then yes, "the" (a) solution to an MINLP is a global optimum (note that some problems have ...
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1 vote

how to implement a constraint with max/min function in pyomo

Maybe you can replace your equality constraint with two inequality $\leq$ and $\ge$ constraints. Also, have a look at this link
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  • 8,290
1 vote

Solving a non-linear non-convex mixed-integer program

Try to take a look at these non-convex programming techniques: DC Programming and DCA http://www.lita.univ-lorraine.fr/~lethi/index.php/dca.html https://link.springer.com/article/10.1007/s10107-018-...
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