Questions tagged [nonlinear-programming]

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

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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. ...
Jacob's user avatar
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Multilinear programming over the simplex

Let $\triangle_3 \in \mathbb{R}^3$ be the $3$-simplex. I am solving a series of multilinear programming problems that looks like this: $$\text{Maximize}\sum_{0\leq i, j, k \leq 3} A_{i,j,k} x_i x_j ...
AspiringMat's user avatar
5 votes
0 answers
463 views

How to write this objective in CVXPY for quasiconvex programming?

I have the following objective that I want to maximize: \begin{equation} \max_{U_T\in \mathbb{R}, x\in\mathbb{R}^T} J_\alpha(U_T) = \frac{\alpha}{\alpha-1}\log\left(\frac{\cosh(U_T)}{\cosh(\alpha U_T)^...
Uomond's user avatar
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2 votes
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log-log regression as reward function in optimization problem

Consider the model $\hat{y}_t = e^{\text{trend} + \text{seasonality}} \prod_k^K x_{k, t}^{b_k}$ where $K$ denotes different investment alternatives. You can think that trend and seasonality are ...
pete lewis's user avatar
1 vote
0 answers
28 views

Steepest ascent vector at a point of a constrained nonlinear problem

I'm looking at this article: "Packing unequal circles into a strip of minimal length with a jump algorithm" (Stoyan et Yaskov, 2014) DOI In section 5, a nonlinear constrained model is ...
fontanf's user avatar
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2 votes
1 answer
129 views

How to model a penalty for exceeding a threshold in a nonlinear optimization problem using IPOPT?

I'm working on a nonlinear optimization problem where I have a decision variable representing my product's price (P_m) and a constant representing my competitor's price (P_c). I want to introduce a ...
MarcM's user avatar
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3 votes
1 answer
60 views

Finding a starting ellipsoid and a minimum volume to approximate a convex optimization problem

Suppose we have a convex optimizatiom program: \begin{align} \min &\quad f_0(x)\\ s.t. &\quad h_i(x) = 0 && i=1,\ldots, p\\ &\quad g_i(x) \leq 0 && i=1,\ldots, m\\ &\...
eden hartman's user avatar
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1 answer
89 views

Algorithms for maximizing the sum of power functions with linear constraints?

I’m working on an optimization problem that arises from maximizing the return obtained from investing in different marketing levers. The return from each lever exhibits diminishing returns, and is ...
Carlos Zanini's user avatar
1 vote
1 answer
66 views

Knitro dimension of lambda for Hessian

I'm trying to supply knitro with a Hessian but struggle to understand the dimension of the Lagrangian multiplier $\lambda$. From my general education and knitro's ...
Frank's user avatar
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Problem in understanding an equation from a paper about iterative Linear-Quadratic Regulator

I'm reading a paper about iterative Linear-Quadratic Regulator (iLQR) and there are a lot of points that I don't understand. https://homes.cs.washington.edu/~todorov/papers/TassaICRA14.pdf I think ...
user900476's user avatar
2 votes
1 answer
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Question About Fritz John Theorem and Slater Constraint Qualification

Background Information I am studying constraint qualifications. Here are two theorems leading to my question: Theorem 1$\space\space\space\space$ [Fritz John Theorem] Suppose that $f, g_1, \dots, g_k$...
Beerus's user avatar
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1 answer
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Is there any literature on constrained nonlinear optimization where constraint returns have to be queried from an oracle?

I am looking at literature considering constrained optimization problems of the form: $\min_{x\in X\subseteq R^n} f(x), \text{ subject to } g_{oracle}(x) \leq 0$ The optimization algorithm doesn't ...
Shourya Bose's user avatar
-1 votes
2 answers
181 views

How do I optimize this problem where the constraints and objective are variable?

Problem Definition: Pa = Constant Pb = Constant Vmax_a = Constant Vmax_b = constant Objective Function: ...
kontrol-c's user avatar
-1 votes
2 answers
105 views

How to maximize sum of cosine squared plus sum of sine squarred?

I want to maximize this function $$\left(\sum_{k=1}^{N}\cos(2\pi f_1t_k+\phi_k+\alpha\pi(k-1))\right)^2+\left(\sum_{k=1}^{N}\sin(2\pi f_1t_k+\phi_k+\alpha\pi(k-1))\right)^2,$$ where the variables are $...
zdm's user avatar
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2 votes
1 answer
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Derivative-free based optimization subject to a linear constraint

I'm dealing with a NLP-problem that can be formulated as: $$\min_{\overrightarrow{x}} f(A\cdot\overrightarrow{x})$$, where $\overrightarrow{x}$ is a vector of $n$ design points where every element ...
Steven01123581321's user avatar
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1 answer
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Knitro`ms_maxsolves` equivalent in Ipopt

Ipopt/Knitro are local optimization solvers, so for nonconvex problems convergence doesn't guarantee optimality. However, Knitro has a multi-start method where one can start with more random initial ...
independentvariable's user avatar
0 votes
1 answer
59 views

Min-convex function as constraint

I have a constraint that is as follows: $$ Ax - f(x) \leq 0 $$ where $f(x)=min_y(g(x,y))$. Which is convex. I can even get the gradient in $x$. How can I reformulate my constraint? or what ...
orpanter's user avatar
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1 vote
1 answer
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$\min\{f(x_1),\dots,f(x_n)\}$ with other constraints

I have an optimization problem which goes: \begin{align*} \text{Minimize:} \\ & \sqrt{x} + \sqrt{y} \tag{NL-objective} \\ \text{Subject to:} \\ &3x + 2y \geq 2 &...
madhafakha's user avatar
0 votes
3 answers
168 views

Using PULP to model machines in a factory

Complete revision: I have all 4 machines that can run in positive and negative directions which results in 2 outputs: $ P_1 = \begin{cases} -390 \le P_1 \le -300 & \text{for neg mode}\\ 0 &...
sino's user avatar
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2 votes
2 answers
123 views

Optimize least squares penalized by curvature of log pdf

I have probability values $p \in \mathbb{R}^n$. Given $A \in \mathbb{R}^{m\times n}$, $b \in \mathbb{R}^m$, I want to minimize the following objective function. $||Ap - b||_2^2 + \sum_{i=1}^{n-2} (\...
JEK's user avatar
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2 votes
2 answers
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Potential methods for solving quadratic optmization problem

I am trying to solve a non-convex optimization problem with the help of sequential quadratic programming. I need to develop an algorithm inside SQP to solve this subproblem. What potential methods (...
Muhammad's user avatar
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0 answers
56 views

How do I solve this non-linear optimisation problem based on simulations?

I have an optimisation problem that is essentially a knapsack problem with a non-linear objective. I have an input dataframe that contains a row for each item, each item has columns defining its mean ...
will's user avatar
  • 31
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1 answer
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Sensitivity analysis for decision vectors in convex programming

Can we perform sensitivity analysis on the decision variables for the perturbed right-hand side of the constraints in a convex/nonlinear program? I know a basic result regarding the sensitivity of the ...
T_k's user avatar
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Resource selection problem with non-linear objective function

I have an optimisation problem to solve but I can't model it correctly. Any insight is welcome :) It has been a few years since my optimisation classes in university, and while I have forgotten a lot ...
Roegel's user avatar
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3 votes
0 answers
77 views

Looking for an efficient way to solve a fractional problem (affine function over euclidean norm )

While working on optimization issues I encountered the following problem: $$\left\{\begin{array}{ll} {\displaystyle \sup_{z\in\mathbb{R}^{m}}} &\frac{ \langle c,z \rangle + \rho}{ \left\|B z\...
Diego Fonseca's user avatar
2 votes
3 answers
169 views

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} ...
Ahmed's user avatar
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1 vote
4 answers
141 views

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 ...
KGM's user avatar
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1 vote
2 answers
109 views

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) ...
Muhammad's user avatar
1 vote
2 answers
574 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 ...
Muhammad's user avatar
2 votes
2 answers
337 views

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, ...
3bod's user avatar
  • 21
1 vote
1 answer
163 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 ...
Reza Farahani's user avatar
1 vote
2 answers
61 views

Solving single-variable fractional equation

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\...
Reza Farahani's user avatar
2 votes
1 answer
122 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: $...
fearloathing121's user avatar
3 votes
1 answer
152 views

Modelling a decision variable as an index of a (fixed) set

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 ...
Steven01123581321's user avatar
2 votes
1 answer
239 views

Implementing a MINLP problem in Pyomo: giving an infeasible solution

I'm trying to implement a MINLP problem which is described in a previous post here: How do we formulate a problem where the decision variable has an index that is also a decision variable? The only ...
Steven01123581321's user avatar
6 votes
3 answers
463 views

How do we formulate a problem where the decision variable has an index that is also a decision variable?

I want to maximize the sum of a nonlinear function $f(.)$ w.r.t. $x$ that is convex in $x$: $$\max \sum_{i=1}^N f(x_i), $$where $x_i$ is a continuous variable and $0 \le x_i < 1$ for $i = 1, 2, \...
Steven01123581321's user avatar
1 vote
1 answer
534 views

OR-Tools: Nonlinear constraints?

I have inherited a reasonably simple ortools-based optimizer (Python) with linear relationships that I need to non-linear-ize, and I have no idea how to do that. The relevant part of my problem looks ...
Matthias Urlichs's user avatar
1 vote
1 answer
131 views

Formulating a continuous NLP problem with a class variable

In this minimization problem we have $N$ items, $j= 1, 2, \dots, N$ and a decision variable $x_j$ which are continuous values. For every item, we have a nonlinear objective function $f$ in function of ...
Steven01123581321's user avatar
5 votes
1 answer
261 views

Optimize selection of metal sheets to keep in stock

I already asked this on stack overflow but just found this forum instead and figured it was more suited here. If this isn't allowed please feel free to tell me and I'll delete the post. I am doing ...
guso141's user avatar
  • 53
-1 votes
2 answers
89 views

How to apply smooth approximation to non-linear complementarity constraints?

$P =$ $ x, if U \geq U^{max} $ $ y, if U^{up} < U < U^{max} $ $ z, if U^{down} < U < U^{up} $ $ \alpha, if U^{min} < U < U^{down} $ $ \beta, if U \leq U^{min} $ Where $P$, and $U$ ...
Ghulam Mohy-ud-din's user avatar
2 votes
0 answers
72 views

Branching the product of binary and continuous variable in Gurobi

I have a binary variable (X) multiplying a continuous variable (Y). I know I can linearize by adding an auxiliary variable (I have that model working), but I now want to do my own branching in the ...
orpanter's user avatar
  • 507
2 votes
1 answer
94 views

Formulate revenue maximization problem and find an appropriate solver

I am trying to maximize expected revenue over a horizon. Consider the following function: \begin{align} sales(budget_1, budget_2) = \sum_te^{C_1t} * budget_1t^{saturation_1t} + e^{C_2t} * budget_2t^{...
jakobhellander's user avatar
4 votes
1 answer
174 views

How to solve a "nearly" linear program

Given a positive integer $n$, a constant $k=2/3$, and $7$ variables $x_1, x_2, x_3, x_{12}, x_{13}, x_{23}, x_{123}$ (non-negative reals or integers) I would like to find: $$\min \binom{x_1}2$$ ...
Fabius Wiesner's user avatar
2 votes
1 answer
112 views

How to mathematically model this multi-objective optimization problem?

I have a system of $M$ machines and $U$ users. Each machine has a capacity in terms of number of resources. Let, machine $m$ has $\zeta_m$ resources. Each user has a service demand $d_u$ and there is ...
KGM's user avatar
  • 2,211
3 votes
1 answer
175 views

How do I pass an objective bound to Gurobi?

I have a non-convex Quadratic Programming over unite simplex set. I have a valid lower bound on the objective function (goal is minimization problem). If I add a constraint like $$f(x)\geq lower~bound,...
Abbas Khademi's user avatar
1 vote
0 answers
56 views

How to avoid complementarity constraints in continuous nonlinear program?

In my two-stage continuous NLP problem, I have a constraint in second stage: $X_{g,k}$ = $X_{g,0} + a_{g} d_{g} $, if $X_{g,k} \in [X_g^u,X_g^l]$ $X_{g,k} = X_g^u$, if $X_{g,k} \geq X_g^u$ $X_{g,k} ...
Ghulam Mohy-ud-din's user avatar
1 vote
1 answer
65 views

An if-then-else logic whose condition is an inequality

I was hoping to get some help in modelling the following logic. I tried to solve it by "Big-M method" but failed. Thank you in advance! $a(k,n)$ and $b(k,n)$ are known constants, $\lambda$ ...
WaMIMO's user avatar
  • 33
-1 votes
1 answer
122 views

Ipopt finds a better solution if I do not eliminate the zeros in the hessian matrix ?(we eliminate the zeros by defining the structure)

I use Ipopt to solve a problem with sparse hessian and jacobian matrices. If I provide the hessian matrix: its structure, and the non zeros elements in the hessian matrix, it will be really fast. If I ...
Hussein Sharadga's user avatar
0 votes
1 answer
106 views

The max_wall_time and max_cpu_time in ipopt are not working?

The max_wall_time and max_cpu_time are not working in ipopt (cyipopt). See example: ...
Hussein Sharadga's user avatar
0 votes
2 answers
98 views

Bellman Equation for nonlinear model

Consider the following model: \begin{align*} max \quad Z &= 19x_1 - 3x_1^2 + 5x_2^2 - x_2^4 + 4x_3 \\ & s.t. \quad x_1 + 3x_2 + 3x_3 \leq 7 \\ & \quad \quad \quad x_1,x_2,x_3 \geq 0 \end{...
OpenAtTheClose's user avatar

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