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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 ...
Alex Shtoff's user avatar
2 votes
2 answers
174 views

Are McCormick Envelopes exact for the following class of optimization problems?

I have the following optimization problem: \begin{align*} \text{minimize} \quad &\mathbf{c^T x} \\ \text{such that} \quad &\mathbf{x} \in S. \end{align*} Here, $S$ is a polyhedron of the form $...
graphtheory123's user avatar
1 vote
2 answers
172 views

Linear approximation of fraction for a maximization problem

I have a problem given as \begin{align*} \underset{\mathbf{x}}{max} & \left|\mathop{\sum_{n=1}^{N}}\left[\frac{\mathbf{a}\left(n\right)}{\mathbf{b}\left(n\right)+\mathbf{x}\left(n\right)}\right]\...
Muhammad's user avatar
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0 answers
51 views

Modeling Approach to Adjust linear Elasticity Effect in Pricing Optimization

I am working on a pricing optimization model for a product where the price depends on the competition as well as our costs. The current formulation of the model is: ...
MarcM's user avatar
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1 answer
45 views

Converting a function composing of multipe pieces into a linear equation

I have a variable (alpha) which depends on some other binary variables, denoted as X_i. So, for some combination of other variables, alpha may take a value (Beta_j). I added some auxillary variables (...
Sam's user avatar
  • 97
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0 answers
49 views

Solving convex separable programming problem using interior point method?

In my engineering application, all decision variables are non-negative and everything is convex separable. In addition to that, the only function that I am trying to approximate with grid point are $f(...
Tuong Nguyen Minh's user avatar
1 vote
0 answers
87 views

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] + ...
MarcM's user avatar
  • 133
2 votes
1 answer
95 views

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,...
Erel Segal-Halevi's user avatar
2 votes
1 answer
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. ...
KGM's user avatar
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3 votes
2 answers
144 views

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 ...
jbuddy_13's user avatar
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2 answers
75 views

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 ...
j x's user avatar
  • 111
-1 votes
2 answers
172 views

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 ...
138 Aspen's user avatar
  • 197
1 vote
0 answers
101 views

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 ...
graphtheory123's user avatar
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0 answers
43 views

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 ...
Lemma's user avatar
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1 vote
0 answers
94 views

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. ...
Dzmitry Lahoda's user avatar
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0 answers
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 ...
Lemma's user avatar
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1 vote
1 answer
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. ...
Jacob's user avatar
  • 111
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0 answers
63 views

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
550 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
  • 86
2 votes
0 answers
98 views

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
171 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
  • 133
3 votes
1 answer
67 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
0 votes
1 answer
93 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
81 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
  • 13
0 votes
0 answers
17 views

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
79 views

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
62 views

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
186 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
138 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
  • 403
2 votes
1 answer
70 views

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
0 votes
1 answer
68 views

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
74 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
  • 517
1 vote
1 answer
57 views

$\min\{f(x_1),\dots,f(x_n)\}$ 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
216 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
  • 1
2 votes
2 answers
130 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
  • 121
2 votes
2 answers
110 views

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
0 votes
0 answers
62 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
1 vote
1 answer
126 views

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 ...
Krypt's user avatar
  • 97
0 votes
0 answers
72 views

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
  • 1
3 votes
0 answers
85 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
225 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
  • 113
1 vote
4 answers
148 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
  • 2,377
1 vote
2 answers
120 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
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 ...
Muhammad's user avatar
2 votes
2 answers
553 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
2 answers
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 ...
Reza Farahani's user avatar
1 vote
2 answers
63 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
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: $...
fearloathing121's user avatar
3 votes
1 answer
215 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

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