The nonlinear-programming tag has no wiki summary.

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### Finding all local maximum points of a function?

Let ${\boldsymbol \theta}=(\theta_1,\theta_2,\ldots,\theta_n) \in{\mathbb T}^n$ and $P:{\mathbb T}^n\rightarrow {\mathbb R}$ be a function defined on $n$-torus as
$$
P({\boldsymbol \theta}) = ...

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**1**answer

319 views

### Finding zeros of a multi-variable nonlinear trigonometric function

I am trying to calculate analytic solution (or locus) of zeros of a very large multi-variable function which is consisted of thousands of nonlinear trigonometric terms. All the variables are real ...

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**1**answer

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### Is the feasibility of a system of nonlinear, non-convex equations (inequalities) decidable?

I would like to know whether the following problem is decidable.
Is the system
$x^T Q_i x + r_i = 0 \mbox{ for } i = 1, ..., k$
$x^T Q_j x + r_j \neq 0 \mbox{ for } j = k+1, ..., t$
feasible, ...

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**1**answer

228 views

### solve non-convex quadratic constrained quadratic programming

$\min_{\beta}\beta^{T} A \beta$
$s.t. \ \beta^{T} C \beta=1\ and\ \beta\geqslant 0$
Here $A,C\in \mathbb{R}^{M\times M}$, $\beta \in \mathbb{R}^{M}$
I saw in one paper saying that it could be ...

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**1**answer

127 views

### Can one always Decide whether a Systems of Nonlinear Equations with Bilinear terms is Feasible?

I have come to a point in my PhD research were i need to prove that a particular decision procedure is decidable or not. And if i can solve the sub-problem described below, i shall have proved it. The ...

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**1**answer

272 views

### Can you maximize the spectral norm of a matrix in a semidefinite program?

Consider the following optimization problem: Maximize $||X||$, subject to $X$ being Hermitian (or symmetric, if you prefer) and a bunch of semidefinite constraints on $X$. I want to know if this can ...

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**1**answer

716 views

### linear objective function, non-linear constraints involving square-root of variables

i am trying to solve a general linear objective function with non-linear constraints. Can someone help me solve this.
Here is an example of one problem i am trying to solve,
minimize $b$
subject ...

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**2**answers

184 views

### what method can I employ to solve this optimization problem which involves \min?

The optimization problem is:
maximize $$\min(\sum\limits_{i=1}^N \log\left(a_{1,i}+\frac{b_{1,i}}{c_{1,i}+d_{1,i}x_i}\right),\sum\limits_{i=1}^N ...

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**1**answer

378 views

### An algorithm for checking if a nonlinear function f is always positive

Is there an algorithm to check if a given (possibly nonlinear) function f is always positive?
The idea that I currently have is to find the roots of the function (using newton-raphson algorithm or ...

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**0**answers

372 views

### Solving a system of complex non-linear equations

I have a set of five equations which can be described as follows:
$m_{i}=\frac{k_{1}}{(x+a)^{i}} + \frac{k_{2}}{(b+d)^{i}}+ \frac{k_{3}}{c^{i}}$
for i=1 to 5 where
$$\eqalign{
...

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**2**answers

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### Solving a system of equations/inequalities that have trigonometric functions on the left-hand side

Is there any known (symbolic) method that solves a system of equations/inequalities that have trigonometric functions on the left-hand side of the system?
Ex) Find $x,y,\theta \in \mathbb{R}$ that ...

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**1**answer

271 views

### A positive semidefinite programming problem

Dear all,
I've got a SDP problem as follows:
$\min_{{\bf H}\succeq0}\quad trace({\bf H}) - {\bf a}^{\top}{\bf H}{\bf b}$,
where ${\bf a}$ and ${\bf b}$ are two constant vectors. May somebody tell ...

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**0**answers

222 views

### Multiobjective semidefinite programming

Let $C$ be size $n \times n^{2}$.
Let $B$ be size $2^{g(n)} \times n^{2}$ where $g(n) > n$.
There is only one $\mathcal{1}$ per row of $C$ and remaining entries of $C$ are $\mathcal{0}$.
$B$ is ...

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**2**answers

479 views

### maximizing multivariate polynomial

Consider $J = \sum_{i=0}^{N}y_{i-1}x_{i}y_{i+1}$ where $+$ and $-$ in the indices are mod $N+1$. Let $x_{i} = 1 - y_{i} \in \{0,1\}$. What are some of the tools useful and relaxation techniques ...

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117 views

### Question on non-linear parametric mixed integer program

I am trying to solve a mixed integer minimization problem, where there are a number of parameters, and there are products of parameters with variables appearing in the objective function. I assume ...

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### Any efficient software/package/toolbox for nonlinear programming for MATLAB

I want to solve a nonlinear programming problem with the objective function being coded as a recursive function in Matlab. I have tried “fmincon”, but it could not get the solution due to large number ...