# Questions tagged [minlp]

For questions about mathematical optimization problems with continuous and discrete variables and nonlinear functions in the objective function and/or the constraints. Should be synonymous with mixed-integer-nonlinear-programming tag.

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### Global Optimization when the exponential function is involved

I wonder if there are methods to determine the global optimum of MINLP problems, when the nonlinear functions involved are only of the form $Z = Y e^{- \alpha X}$, where $Y \ge 0$ and $X \ge 0$. Are ...
63 views

### MINLP Solution same as Global Optimum?

Is the solution to an MINLP problem the global optimum to this problem?
101 views

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

I am implementing a NLP problem in pyomo, and I am getting some issues for this constraint: \begin{equation} \forall i \in \lbrace 1, N \rbrace , \forall j \in \left\{1, M \right\}: Y_{i,j} \cdot ...
80 views

### How to define hybrid variables without using additional binary variables?

I am working on a large NLP model with equilibrium equations in which the variables are defined in the following form: x_i \in [L_B, U_B] \cup\{0\} \quad \text{where} \quad L_B \ \& \ U_B \in\...
101 views

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

I am using Knitro to solve an MINLP using branch-and-bound and I want to know about the reference or technique they are adopting to code their algorithm. I know that there are many applications of ...
128 views

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

The optimization problem that I am dealing with is very similar to this example. In brief, I have some decision variables that can take real values with lower/upper bounds, and some other variables ...
80 views

### Is there a library of infeasible MINLP problems?

We have a number of test libraries to test solver performance like MINLPLIB, QPLIB, etc., but the problems in all libraries I know are overwhelmingly on the feasible side. Is there a library to test ...
237 views

### Do the KKT conditions hold for mixed integer nonlinear problems?

I was wondering if the KKT conditions are applicable for for MINLPs, and if not, why not? What about the case when the integer variables are modeled using constraints involving just continuous ...
240 views

### Understanding why this MINLP formulation is infeasible

Algebraic Formulation - Note: All parameter values are subject to change, I have just used the numbers you see here as place holders for the time being. Additionally, there are a few other equations ...
185 views

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

I am trying to write out a MINLP problem of optimal control for an invasive species and the code that I have for my PYOMO model is below. Some of the initialization values take from an Excel ...
386 views

### Formulating a MINLP for CPLEX in PYOMO

I am trying to do my first MINLP problem using PYOMO and CPLEX - although I am not committed to using CPLEX, but it was recommended to me. To my understanding you need to formulate your problem in ...
What (deterministic) global optimization packages support trigonometric functions such as $\sin, \cos, \tan$ in the constraints or objective function? What limitations do they have? I am not asking ...