# Questions tagged [nonlinear-programming]

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

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### Modeling $-\ln(1 - w \cdot \sigma(x))$ as disciplined convex programming

Given $0 < w \leq 1$, I would like to use the function: $$-\ln(1 - w \sigma(t)),$$ where $\sigma(t) = 1 / (1 + \exp(-t))$ is the sigmoid function, in my objective. It's a bit tedious, but this ...
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174 views

1 vote
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### volume-weighted mean equality constraints

I have the following optimization objective function for a dynamic pricing problem: \begin{align*} sum\_profit = \sum_{i \in sales\_point} \Bigg( constant[i] + {elasticity[i]} \cdot (movement[i] + ...
• 133
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### Are there classes of non-linear programs that always have sparse solutions?

It is well-known that linear programs always have sparse solutions -- solutions in which only at most $m$ variables are nonzero, where $m$ is the number of constraints. In the answers to this question,...
213 views

### How to transform a binary QP into an MILP?

I have a binary quadratic problem with objective ${\bf{x}}^T{\bf{Qx}}+{\bf{c}}^T{\bf{x}}$ subject to ${\bf{A}}{\bf{x}}\le{\bf{b}}$ ${\bf{A}}_{eq}{\bf{x}}={\bf{b}}_{eq}$. here ${\bf{x}}$ is binary. ...
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### Lagrangian Multipliers for constraints in nonlinear optimization problems?

Suppose I want to optimize some function of continuous variables and the objective is nonlinear; in this context, gradient-based methods are quite popular. To my knowledge, soft constraints can be ...
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1 vote
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### How to maximise black-box function defined on a subset of integers, with access to its derivative?

The basic form of my problem is as follows. Let $S = \{ 1, 2, ..., 30 \}$. I have an integer-valued function $f$, whose argument is an integer-valued vector $\vec{x} \in S^{200}$. I also know that ...
• 111
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### How to describe nonlinear programming in gurobipy?

The optimization task The optimization task concerned here is: A square matrix $A\in \mathbb{R^{5\times 5}}$ satisfies the condition: the elements of the first row all are 1, the elements of the ...
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1 vote
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### Converting a Linear Program with TU Constraint Matrix to a Nonlinear Convex Model: Solver Performance?

I'm currently working on a large Mixed Integer Program (MIP) where the constraint matrix is Totally Unimodular (TU), allowing me to model it as a Linear Program (LP) for efficiency, as total ...
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### Using Knitro or Xpress SLP via FICO Xpress Python API for Local and Global Solve Methods

Can someone guide me on how to utilize the FICO Xpress Python API to invoke Knitro or Xpress SLP, specifically for choosing between local and global optimization methods? I am referring to the version ...
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1 vote
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### Numerical infeasibility for moving numbers along some specific conversion edges to get maximal number on target node from some starter node

I have a problem that can be represented as an optimization problem. Sometimes, solver engines report infeasible depending on the parameters I have at hand. The root cause is numeric ranges. ...
58 views

### Better formulation of bilinear terms

I am working on an optimization problem where I need to formulate a constraint that represents the total sales value under specific conditions. The challenge lies in creating an expression that ...
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1 vote
123 views

### Maximizing sum of probabilities with variable distributions

Suppose $\\{X_i\\}$ are binary decision variables and $\\{A_j\\}$ are Skellam random variables with $(\mu_1, \mu_2) = (\sum_i b_{i} X_i, c_j)$. Here, $b_i, c_j \in \mathbb{R}^{\geq 0}$ are constants. ...
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### Linearization the product of three variables (two binary & one continuous)

Consider the following binary variable $x \in \{0,1\}$ and two continuous real variables $y,p \in \mathbb{R}$. I am trying to model the following conditional equations as constraints: \begin{cases} ...
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1 vote
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### How to perform clustering of a large number of nodes?

I have a clustering problem with around 400-500 nodes. The edge between any two nodes has a weight (between 0 and 1, 0: can be considered as there is no edge/connection between these two nodes) as ...
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1 vote
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### My barrier function is always giving a complex number

I am working on implementing the interior point method, and the barrier function always gives me a complex number. B(x) = f(x) - t * sum(ln(hi(x))). I have changed the value of 't' to see the B(x) ...
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1 vote
602 views

### Non linear programming

I want to solve a large scale non linear optimization problem and there are two methods interior point method and sequential quadric programing usually used to solve non linear optimization problem. I ...
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### I want to solve an optimization problem with nonlinear piecewise objective function (I tried Pyomo with "ipopt" solver but I had an error)

I want to solve an optimization problem where the objective function is the summation of nonlinear, piecewise functions in the decision variables q_i's such that when a decision variable q_i < 1, ...
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219 views

### Nonlinear fractional objective function

Could you please teach me when an optimization model with fractional terms in the objective function can be linearized or solved optimally? I only know that if the objective function has a single ...
1 vote
Can anyone advise how this nonlinear equation with a single variable $x$ can be solved as a closed form? ${\left(\frac{x}{1-x}\right)}^2.{\left(\frac{x-C}{\left(1-x\right)-N}\right)}^2=H.\frac{2x-C}{2\... 2 votes 1 answer 129 views ### Formulation of nonlinear nonconvex optimization problem and finding appropiate solver Consider the notation and objective below for this sequential resource allocation problem: Allocation channels$i \in (1, 2)$Spend/Cost timestep i channel j:$C_{i, j}$Total resource:$B$Horizon:$...
I'm trying to model the following MINLP problem in Pyomo. We are trying to minimize a nonlinear objective function $f$ in $x_i \in \lbrace{0, 1, 2\rbrace}$ for $i= 1, 2, \dots, N$ and subject to a ...