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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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13 votes
4 answers
840 views

What global MINLP solvers support trigonometric functions?

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 ...
Michael Feldmeier's user avatar
12 votes
1 answer
154 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 ...
Nikos Kazazakis's user avatar
10 votes
1 answer
4k views

What are good reference books for introduction to operations research?

The reference books should cover the wide range of problem-solving techniques and methods.
Rajasekhar Kadambur's user avatar
9 votes
1 answer
904 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 ...
Josh Allen's user avatar
9 votes
2 answers
210 views

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

INTRODUCTION My research often involves solving MINLP problems with few constraints (usually two) and not many variables (say between one and three integer ones, and between one and five real-valued ...
Vicent's user avatar
  • 191
9 votes
2 answers
607 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 ...
GrayLiterature's user avatar
8 votes
1 answer
652 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 ...
GrayLiterature's user avatar
8 votes
1 answer
888 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 ...
GrayLiterature's user avatar
5 votes
3 answers
597 views

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 ...
Clement's user avatar
  • 2,252
5 votes
2 answers
171 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 ...
Math is fun's user avatar
5 votes
2 answers
504 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 ...
V-Red's user avatar
  • 239
3 votes
2 answers
370 views

Can we use continuous variables instead of binary variables in this NLP problem?

The following problem is defined with binary variables $a_{i1}, a_{i2}, a_{i3}, k_1$ and $k_2$. Is it possible to avoid binary variables and to only work with continuous variables? How would we ought ...
Steven01123581321's user avatar
3 votes
1 answer
305 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\...
Oguz Toragay's user avatar
  • 8,667
3 votes
1 answer
3k 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 ...
Betty's user avatar
  • 544
3 votes
0 answers
232 views

Solving a nonlinear model with constraints of exponential functions and continuous variable multiplications

I have a nonlinearly-constrained model and wonder if a nonlinear solver like Ipopt or Knitro can solve the problem. Briefly, my objective function is linear. I have the following variables with their ...
tcokyasar's user avatar
  • 1,249
2 votes
1 answer
87 views

How to define a stationary point of the MINLP problem?

As we all know, KKT point and stationary point are well defined when the optimization variables are continuous in the problem. Now, I want to know whether there exist some special points except for ...
fengbiqian's user avatar
2 votes
2 answers
134 views

MINLP Solution same as Global Optimum?

Is the solution to an MINLP problem the global optimum to this problem?
Clement's user avatar
  • 2,252
2 votes
1 answer
109 views

Structuring an MINLP solver

Folks, I am working on a project in which I have to code some C++ algorithms for smooth MINLPs. Such algorithms are Extended Cutting Plane, Extended Supporting Hyperplane, and Outer Approximation. I ...
Matheus Diógenes Andrade's user avatar
2 votes
1 answer
283 views

Large MINLP problem, searching for solver, tried BARON, ANTIGONE, DICOPT

I am working on a MINLP problem and am searching for a solver that works. I have tried ANTIGONE and receive the following "Termination Status: Infeasible Problem." I also tried DICOPT which ...
Devon Elizabeth's user avatar
2 votes
0 answers
76 views

Benders with MINLP subproblem as the pricing problem of Dantzig Wolfe

I have a convex MINLP that after a Dantzig-Wolfe reformulation, passes most of the difficulty onto the pricing problem, which becomes a convex MINLP itself. The pricing problem should be solvable with ...
J. Dionisio's user avatar
2 votes
0 answers
134 views

Defining a highly non-linear function of integer variables

I have a complicated non-linear objective function of positive integer variables subject to linear constraints: $\mathop {Min}\limits_{\underline x} f(\underline x)$ s.t. $A\underline x\leq \underline ...
Johnthemathematician's user avatar
1 vote
1 answer
30 views

Traverse discrete approximations to a continuous system

I have a system of equations looking like $$ \frac{2.8 R_{6}}{R_{4} + R_{6}} = \frac{5.2}{\left(\frac{1}{R_{2}} + \frac{1}{R_{1}}\right) \left(R_{7} + \frac{1}{\frac{1}{R_{2}} + \frac{1}{R_{1}}}\right)...
Reinderien's user avatar
1 vote
0 answers
46 views

Seeking Assistance with Applying Benders Technique for Bilinear Problem Solving

I have two specific types of bilinear terms in the problem. The first type involves the multiplication of an integer variable and a continuous variable, while the second type involves the ...
Samira Fallah's user avatar
1 vote
2 answers
175 views

How to formulate this NLP problem correctly?

Current status on the problem (what I've done) I'm working on a NLP problem and I got a formulation of the problem, together with the necessary constraints, but I think it needs some adjustments to ...
Steven01123581321's user avatar
0 votes
0 answers
25 views

Differences between non-convex and convex optimization problem with l0-Norm Regulization

I'm currently in the process of writing my bachelor's thesis and trying to deal with the theory behind the model in this paper Risk-calibrated Super-sparse Linear Integer Model (Berk Ustun and Cynthia ...
user13121's user avatar