We’re rewarding the question askers & reputations are being recalculated! Read more.

# Questions tagged [optimization]

Optimization is the process of choosing the "best" value among possible values. They are often formulated as questions on the minimization/maximization of functions, with or without constraints.

14,752 questions
Filter by
Sorted by
Tagged with
3 views

### Benchmark/standard bang-bang optimal control example

So I was just curious if someone could give me a reference of a standard bang-bang control problem. I would very much like a problem where there is an analytic solution for the state and the control. ...
7 views

### Related Rates/Optimization Help

(This is a weird one) - (given information comes after question $1(b)$ $1(a)$ You're listening to country music and drinking a beer in your above ground pool/watering trough shaped like an inverted ...
8 views

I trying to minimize this objective function. $$J(x) = \frac{1}{2}x^THx + c^Tx$$ First I thought I could use Newtown's Method, but later I found Gradient Descent, which is more suitable for this ...
5 views

### Cross validation multivariate kernel regression in R

This question is general- I have a data set of n observations, consisting of a single response variable y and p regressor variables ( here, n ~50, p~3 or 4). I am planning to implement Nadaraya-Watson ...
18 views

### Show that Lagrange multiplier is the optimal value

I am trying to solve the following problem. Minimize $$f(x,y) = x^2 + y^2$$ Subject to $$g(x,y) = ax^2 +2bxy +cy^2-1 = 0$$ $$(x,y)\in\mathbb{R^2}$$ Where $$a>0,c>0,2b>a+c$$ a) Use Lagrange ...
2 views

### Measurability of the Knothe-Rosenblatt (rearrangement) transport map in Optimal Transport

Allow me to explain the setup first: Let $\mu(dx_1,dx_2) = f(x_1,x_2)dx_1dx_2$ and $\nu(dy_1,dy_2) = g(y_1,y_2) dy_1dy_2$ be two probability measures on $(\mathbb{R}^2, \mathcal{B}(\mathbb{R}^2))$ (...
39 views

19 views

### Show that Each LP problem in standard form enjoys the following three properties? [on hold]

a. if LP problem has no optimal solution, then it is either infeasible or unbounded? b. if LP problem is feasible, then it has a basic feasible solution? c. if LP problem has an optimal solution, ...
10 views

### How to create a penalty function in two dimensions for a profile curve?

I have a computer model that models a physical process that is represented by the black line shown in the attached figure Desired Result. A traditional penalty function would compare the individual $Y$...
41 views

### Backtracking Line Search Algorithm - Why make $a$ smaller every time?

I am studying line search methods and I stumbled upon the "backtracking algorithm" for calculating a step length $a_k$ that gives a sufficient decrease in our function. To actually compute this ...
11 views

### exists r > 0 such that ∇2f (x) > 0 for any x ∈ B(x0,r).

Let f : U ⊆ Rn → R be a twice continuously differentiable function. Let x0 be an interior point of U such that ∇^2f(x0)> 0(hessian). Prove that there exists r > 0 such that ∇2f (x) > 0 for any x ∈ B(...
38 views

### Why is this limit equivalent to the max? [duplicate]

Reading this paper on the Adam optimizer, I can't see how the step from equation 10 to 11 happens... (https://arxiv.org/pdf/1412.6980.pdf)
33 views

### Struggling to find a convex formulation of a bilinear constraint

I've run into a wall in formulating a convex program for finding equilibria in an economic model I've been working on. I have one bilinear/quadratic constraint left that is getting in my way. Any ...
13 views

### Optimization with positive slope solution

Provided the following parameters: 1. $c_{n}$ and $c_{0}$ are known constants and can't be optimized 2. $c_{1}$ through $c_{n-1}$ are bounded by $[c_{0},c_{n}]$ 3. $\forall(c_{i} - c_{i-1}) \geq 0$ ...
10 views

### how does method of multipliers solve the problem of unboundedness of lagrangian and non differentiability of dual problem

$L_ρ(x,z,y) = f(x) + y^T (Ax − b)+\frac{\rho}{2}||Ax - b||2$ $g(y) = \text{min}_x\{L_ρ(x,y)\}$ Method of multipliers claims to have good convergence properties but I wonder how it solves the ...