# Questions tagged [global-optimization]

The tag has no usage guidance.

214 questions
Filter by
Sorted by
Tagged with
23 views

### How to prove the convergence of Gechberg-Saxton algorithm?

I just have a problem that Gerchberg-Saxton algortihm is no worse than the previous iteration but not sure whether it is convergent.
70 views

### Relations between non-negativity of multivariate polynomials and SOS over gradient ideal

We know there is a necessary condition for the non-negativity of multivariate polynomials in the paper "Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational ...
• 59
1 vote
83 views

### optimization over moving domains

Let $A, B$ be Banach spaces, and for any $a\in A$, $B_a\in B$ is a measurable subset. Consider the following optimization problem: $$L(a)=\inf_{b\in B_a}\ell(b),$$ where $\ell(b)$ is a infinite-times ...
• 87
229 views

• 21
1 vote
63 views

### Estimate of minimum of the Poisson integrals corresponding to a convergent Hausdorff sequence of smooth bounded domains from below

Let $\{\Omega_{j}\}_{j\in\mathbb{N}}$ be a sequence of smooth bounded domains in $\mathbb{C}^{n}$ such that $\Omega_{j}$ converges to a smooth bounded domain $\Omega$ in the sense that the defining ...
• 63
1 vote
119 views

### How to solve the optimization problem $\max_{\mathbf{w}}\sum_i\text{sign}(\mathbf{w}^T \mathbf{x}_i)$?

I am looking for an algorithm to solve the following optimization problem $$\max_{\mathbf{w}}\sum_i\text{sign}(\mathbf{w}^T \mathbf{x}_i)$$ where $\mathbf{w}$ and each $\mathbf{x}_i\in\mathbb{R}^d$. ...
• 175
97 views

### Local behavior around critical points in high dimensions

I have asked this question on math.stackexchange.com but even though I gave a bounty, I was not able to receive any answers at all, so I'm posting it here again, hoping that the question is not too ...
• 419
1 vote
97 views

• 6,824
1 vote
46 views

### Problems with known optimal solution [closed]

I am looking for some problems in which we know the value of optimal solution and should find just a vector of variables. For example in N-Queens problem we know the value of optimal solution (that is ...
• 11
292 views

### Trying to prove an inequality

I am working on a problem and for that purpose, I need to prove the following inequality. Let $t\in [0,1]$ and set $$z_0=1-4t(1-t)\sin^2(4x)\\ z_1=1-4z_0(1-z_0)\sin^2(3x)$$ I need to show that for ...
• 617
68 views

### Optimize a function with not-full knowledge of gradient

I want to optimize the following function: $$argmin_{x} f(x) = g(x) + h(x)$$ , where I can get $\nabla_xg(x)$, but cannot calculate $\nabla_xh(x)$. The derivative-free method, such as the Hill ...
125 views

### Minimax problem : uniqueness of a solution

Let $n\geq2$. Is it true that the minimax problem: $$\min_{p\in\mathcal{P}}\max_{H\in\mathcal H}p^tH\bar{p},$$ where $\mathcal H\subset\mathcal{M}(n)$ is a strictly convex bounded subset of ...
• 3,924
98 views

216 views

• 377
90 views

### Do Pareto critical points of a multicriteria optimization problem form an attractor of the dynamical system induced by a descent algorithm?

Let $d\in\mathbb N$, $k\in\mathbb N$ and $f:\mathbb R^d\to\mathbb R^k$ be differentiable. Say that $v\in\mathbb R^d$ is a descent direction at $x\in\mathbb R^d$ if ${\rm D}f(x)v<0$ (component-wise) ...
• 157
145 views

### What to call a function that is negative on a set

Let $Y$ be a nonempty region in $\mathbb{R}^n$. I am designing an algorithm which given a point $x_0$ outside $Y$ in a finite number of steps lead to a point $x_n∈ Y$. The way I do it is that I have a ...
228 views

### Minimizing the largest eigenvalue of matrix product

Let $A\in\mathbb{C}^{m\times n}$, $B\in\mathbb{C}^{n\times k}$, $C\in\mathbb{C}^{k\times m}$ be given complex matrices. The objective of the optimization problem is \mathop {\arg \min ...
• 377
492 views

### Can solutions to Thomson's problem have pentagons?

Thomson's problem asks for the minimum-energy configuration for $N$ electrons on a sphere (refs: https://en.wikipedia.org/wiki/Thomson_problem, https://sites.google.com/site/adilmmughal/...
• 1,203
301 views

### Gradient-descent "type" Methods for non-convex and non-smooth functions

Most (stochastic) "gradient descent" type algorithms (such as Nesterov-accelerated gradient-descent or ADAM) seem to be well-defined only for functions which are either: lower semi-...
• 5,079
153 views

260 views

### When is the optimum of an optimization problem affine in the constraint parameter?

While working on a variational problem I have reached to the following question: Let $f:(0,\infty) \to [0,\infty)$ be a $C^1$ function satisfying $f(1)=0$. Suppose that $f(x)$ is strictly increasing ...
• 6,651