# Questions tagged [nonlinear-programming]

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

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### Prove NP Hardness for non-convex multi-objective optimization

The multi-objective optimization problem in my case is non-linear as it consists of three objective function of which two are nonlinear function and the third is a linear function. Lets say objective ...
79 views

### Maximization of a differentiable and nonlinear function over a bounded space

I have a nonlinear bi-variate optimization problem like $\max \: f(x,y)$ where $f(x,y)$ is a nonlinear and differentiable function of both variables, and $0\le x\le 1$, $\:0\le y \le ub$. In order to ...
56 views

### Subtracting Values from a Positive semidefinite Matrix in a Semidefinite Program

I'm trying to construct an SDP relaxation for a non-convex quadratic program ($x^{\intercal}\mathbf{H}x$) with the following objective function: x_{11}y_{11} + x_{12}y_{12} + x_{21}y_{...
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### Solver issue? Xpress (slp) - Nonlinear - Python - Pyomo

I tried solving my model with xpress: pip install xpress And then in the model: ...
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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 ...
75 views

### 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-...
163 views

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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 ...
57 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 ...
77 views

### 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., ...
104 views

### 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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I have a system in which I want to maximize the value of some function $f(x_T, y_T)$. The time evolution of the system is described by some functions: \begin{align} \frac{dx}{dt}&=\alpha \frac{... 2answers 146 views ### Constraint x'Ax = 0, where x and A are both optimization variables I'm trying to solve the following optimization problem: \min_{x, \phi} x \quad \text{s.t.} \quad \sum_{s,t = 1}^n \left(m_{s,t} x -v_{s,t} \right)\phi_s \phi_t = 0 , \quad \lVert \phi \rVert = 1... 6answers 2k views ### Nonlinear integer (0/1) programming solver I have the following optimisation problem.\begin{align}\max&\quad\sum_i\sum_j\sum_k x_{ji}y_{kj} \operatorname{cost}(i,k)\\\text{s.t.}&\quad\sum_j x_{ji}=1\quad\forall i\\&\quad\sum_k y_{... 1answer 104 views ### Minimizing sum of functions with pairwise dependence I have formulated a problem where I need to minimize the sum of N functions, with only pairwise dependence between the functions (any single constraint involves only two functions having adjacent ... 1answer 94 views ### Does strong duality hold when I dualize only a subset of the constraints? Suppose I know that for some non-convex program: \begin{align}\min_x&\quad f(x)\\\text{s.t.}&\quad g_i(x)\leq 0, i \in C\end{align} strong duality holds for this problem. Now, suppose I form ... 0answers 48 views ### Linearisation using SOS2 I am trying to linearise the following expresssion. C(k) = B(k) e^{-d(k)}, B(k) \ge 0 , d(k) \ge 0  I am trying to do this by using SOS2 sets. I set X(k) = e^{-d(k)} and I get C(k) = B(k) X(... 2answers 159 views ### Find Euclidean sub-distances for a given distance matrix Assume I have a matrix (d_{ji})_{ij} of distances between points i and j. These distances could be anything fulfilling the triangle inequality. Now I would like to find coordinates (x_i,y_i) ... 0answers 134 views ### Gurobi is unable to give an optimal solution even when it exists I am trying to solve Logarithmic Fuzzy Preference Programming (LFPP) for criteria weight evaluation, based on fuzzy comparisons between criteria, and I am solving it with Gurobi in Python 2.7. It is a ... 1answer 90 views ### Simple nonlinear programming using convexity analysis and KKT I want to solve the following two-variate nonlinear programming using KKT conditions: \begin{align} \begin{split} \max \quad & 15 \sqrt{x_{1}} + 16 \sqrt{x_{2}} \\ \text{s.t.} \quad &...
Optimization of a simple expansion problem minimise: $$\sum_{t=1}^{5}\left[\sum_{i=1}^{2}x_{i,t}CC_i\left(\frac{1+EIC}{1+r}\right)^t+UE_t*C_{UE}\right]$$ subject to:  0 \leq x_{i,t} \leq 5 \\ ...