1
vote
1answer
39 views

Optimization of several cost functions together

Say I want to minimize several functions together: $$\min \lVert f_1\rVert, \min \lVert f_2\rVert, \min \lVert f_1-f_2\rVert$$ where $\lVert f\rVert$ is the $L_2$ norm of $f$. I am wondering can I ...
8
votes
1answer
168 views

Stochastic gradient descent for convex optimization

What happens if a convex objective is optimized by stochastic gradient descent? Is a global solution achieved?
1
vote
1answer
83 views

Computation Effort of Algorithms

Consider the strictly convex unconstrained optimization problem $\mathcal{O} := \min_{x \in \mathbb{R}^n} f(x).$ Let $x_\text{opt}$ denote its unique minima and $x_0$ be a given initial approximation ...
0
votes
0answers
11 views

Variation of Optimal Solution with other Parameters

I have the following kind of optimization problem. $$\min_{f_1,f_2,\cdots\ ,f_L}\sum_{i=1}^L \mu_{i}D_i(\lambda_i,f_i,\gamma)$$ sub. to $$\sum_{i=1}^Lf_i=1-\delta\\ f_i\ge 0\quad i=1,2,\cdots \ ...
1
vote
1answer
63 views

A minimization problem

Define $$L(w,u)=\frac{1}{2}\|w-u\|^2+\beta \left\|\frac{w}{x}\right\|,~w,u\in \Bbb{R}^n$$ where $$\frac{w}{x}=\left(\frac{w_1}{x_1},\ldots, \frac{w_n}{x_n}\right)$$ $$\|x\|=\sqrt{x_1^2+\cdots+x_n^2}$$ ...
1
vote
1answer
45 views

A minimization problem [duplicate]

Define $$L(w,u)=\frac{1}{2}\|w-u\|^2+\beta \|\frac{w}{x}\|,~w,u\in R^n$$ where $$\frac{w}{x}=(\frac{w_1}{x_1},\dots, \frac{w_n}{x_n})$$ $$\|x\|=\sqrt{x_1^2+\cdots+x_n^2}$$ Given $u$, $x$ and $\beta$, ...
1
vote
1answer
137 views

formulate this scheduling problem as linear programming problem

Sorry if this very silly, but i am something new to optimization theory: We have $m$ identical Machines and $n$ jobs. A job $j$ can be done in any of the identical machines in $p_{j}$ time units. ...
1
vote
1answer
94 views

Removing redundant half-spaces that bound a convex polytope

I am computationally representing a convex polytope in $\mathbb{R}^n$ as a set $A$ of half-spaces that bound it; each such half-space is represented by a row vector $\mathbf{v} = \begin{bmatrix}v_1 ...
2
votes
1answer
196 views

Maximal mapping of a convex set to the unit disk

EDIT: To make my question more precise i think we can narrow it down to this. Say you have a simple polygon that includes the origin, that is completely contained in the unit disk, we can 'blow up' ...