0
votes
1answer
48 views

Solving LP with two $L_1$ inequality constraints

Is there a "fast" way to solve the following LP formulation with the following constraints: $$ \max_{\mathbf{f}} \mathbf{f}'.\mathbf{g} \\ \mathbf{1}'\mathbf{f}=1\\ \|\mathbf{f}-\mathbf{h}\|_1\le ...
2
votes
0answers
28 views

Finding optimal hyperplane

I have a set of vectors $\{V_i\}$ in $n$-dimensional space. There is a number corresponded to each vector $\alpha_i = f(V_i)$ ($\alpha_i$ can be negative). I want to find a hyperplane which would ...
1
vote
0answers
43 views

Linear Programming, Optimal Solutions

I posted the whole question to give some context, but my problem lies with (iv). I think you're meant to use a formula for the generalization of the optimal solution, but I'm not really sure what ...
1
vote
0answers
44 views

Maximize minimum optimization using linear integer programming

I am trying to solve a maximize minimum optimization. I have four different items that each of them has 10 values of Rates and for each value it has a corresponding weight. Then I have a free table ...
3
votes
1answer
60 views

Rewrite constrained optimization objective

I wanted to ask, under which conditions can one rewrite the optimization objective $\min_x f(x)\;\;\;s.t.\;\;\;g(x) \leq s$ as $\min_x g(x)\;\;\;s.t.\;\;\;f(x) \leq t$ I have particular interest ...
3
votes
1answer
118 views

Solving ill posed linear equations

Given a set of linear equations $AX=B$, say $A$ is an ill posed matrix (has a few singular values equal or very close to zero), which numerical algorithm (conjugate gradient, least squares or steepest ...
0
votes
0answers
285 views

Can this non-linear optimisation problem be converted to a linear?

I have to minimize the function: $F(x)$ $F(x) = \sum_{i=1}^{M}||x_{i+1} - x_i - K(\frac{x_{i+1} + x_i}{2})||^2 + ||x_1-c_1||^2 + ||x_N-c_2||^2$ , where $x$ is a vector of $N$ scalars, $c$ are ...
1
vote
1answer
129 views

Optimization for large scale linear problem with equality constraint

Given the wide range of optimization methods, which is the appropriate method to use? I am thinking of using either linear programming (interior-point methods) or augmented Lagrangian methods. Which ...