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4
votes
1answer
254 views

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}) = ...
2
votes
1answer
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 ...
1
vote
1answer
113 views

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, ...
0
votes
1answer
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 ...
0
votes
1answer
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 ...
1
vote
1answer
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 ...
1
vote
1answer
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 ...
1
vote
2answers
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 ...
2
votes
1answer
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 ...
1
vote
0answers
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{ ...
2
votes
2answers
1k views

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 ...
1
vote
1answer
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 ...
1
vote
0answers
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 ...
1
vote
2answers
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 ...
0
votes
0answers
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 ...
-1
votes
2answers
418 views

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 ...