# Questions tagged [nonlinear-programming]

For questions about mathematical optimization problems involving a nonlinear objective function and/or nonlinear constraints.

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### Lagrangian dual function of KKT

I encountered a nonlinear problem with a non-convex objective function and an equality constraint, so to decide whether there exist a global optimal, I was told to compute the Lagrangian dual function....
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### How to calculate the time complexity of a Heuristic Algorithm?

I have a binary integer programming problem. I solve it with a heuristic approach. How can I calculate the time complexity of the heuristic algorithm?
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### Water quality component optimization

I have an optimization problem that I'm attempting to tackle. As you can see in the image below, there's a graph network through which water flows. I've drawn out the problem in the image to explain ...
132 views

### Two equivalent soft constraint implementations

Take the following optimization problem: \begin{align}\min_x&\quad f(x)\\\text{s.t.}&\quad g(x)\le0\end{align} with $f$ and $g$ nonlinear functions. Suppose I want to relax the constraint by ...
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### How to solve this clustering problem with heuristic or meta-heuristic approach?

I have clustering problem with servers and users. This is different to the one posted in https://math.stackexchange.com/questions/4088441/what-will-be-an-efficient-joint-clustering-solution-to-this-...
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### Trustful Nonlinear Programming

Is it possible for an NLP solver to claim that a knowingly feasible problem is infeasible? Shouldn't the solver be able to provide a solution (of course not necessarily the global optimum but a ...
56 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 ...
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### Smooth approximation of $\max(f_1(x),f_2(x),\cdots,f_n(x))$

In the GAMS documentation concerning non-smooth optimization I found the following statement: A smooth approximation for $\max(f(x),g(y))$ is as in the following example code: ...
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### Maximize $\sum_{i=1}^n 1/x_i$ subject to an SDP constraint

I would like to solve the following problem: \begin{align}\max_{x_1, \ldots, x_n}&\quad\frac{1}{x_1} + \frac{1}{x_2} + \cdots + \frac{1}{x_n}\\\text{s.t.}&\quad\sum_{i=1}^n x_i A_i \succeq A_0\...
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### Scheduling Problem With Identical Machines

I am working on a nonlinear scheduling problem that minimizes the electricity cost of a facility. This system includes a number of identical machines that consume power and produce a product. When the ...
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### Doesn't Pyscipopt handle nonlinear objective functions?

I am trying to solve a large-scale nonlinear problem. Below is the objective function coded for pyscipopt. I have some loops over a list of tuples (r,p,s) in the list RouteTimeStop, and the only ...
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### Ipopt (probably) fails to solve a nonlinear problem, what is next?

I am trying to solve a nonlinear problem with only a set of continuous variables (where the nonlinearity stems from negative inconsistent - across differently indexed variables - large powers), e.g., ...
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### Solve nonlinear programming problems practically

In an exam, I studied Theoretical approaches to converting constrained minimum problems into unconstrained minimum problems. Specifically: KKT conditions Projection Gradient Descent Penalty and ...
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### Deep Reinforcement Learning for General Purpose Optimization

Recently, I attended a very nice talk given by someone at the place I work about applying Deep Reinforcement Learning (DRL) for a design optimization problem. It was particularly interesting to me ...
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### Optimizing black-box finite element model

I'm trying to understand what my options are for optimizing a black-box simulation (output from a commercial, closed source finite element solver). An example problem is the following. We have a ...
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### Free solver for MINP problems

I have a mixed-integer nonlinear programming (MINP) problem. Is there a free solver for such a problem?
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### Contiguous service area constraint

Background: I have a set of ZIP codes (e.g., all of the state of Wisconsin), and am trying to figure out an optimization-based approach to identify a subset of these ZIP codes for a logistics service ...
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