# Questions tagged [oc.optimization-and-control]

Operations research, linear programming, control theory, systems theory, optimal control, game theory

752
questions

**1**

vote

**0**answers

27 views

### Can we reduce the maximization of this integral to the maximization of the integrand?

I would like to know whether we are able to reduce the following optimization problem to the pointwise optimization of the integrand (or how we can solve it otherwise): Maximize $$\sum_{i\in I}\sum_{j\...

**2**

votes

**0**answers

46 views

+50

### Interesting questions for inverse parabolic problems

I'm looking for some interesting questions and maybe open problems in inverse problems theory, especially in the framework of parabolic PDEs (basically the heat equation). As key words here we can ...

**0**

votes

**1**answer

37 views

### How do I solve this integer programming problem with non convex constraints?

I am not sure if this is the right place to post this question, please point me to the correct forum if I posted in a wrong place.
I have an optimization problem like this
...

**-1**

votes

**0**answers

35 views

### KKT conditions for discrete set [on hold]

Consider the following simple minimization problem:
$$
\min_{x\in\{-1,1\}}x \\
s.t.\ x\geq0
$$
Clearly the constraint $x\geq0$ is inactive, but when you remove it from the Lagrangian (i.e. by setting $...

**0**

votes

**0**answers

54 views

### How can we analytically solve this max-sum-min problem?

Let $I$ be a finite set, and $A_{ij},B_{ij},x_i,y_j\ge0$. I want to find the choice of $x_i,y_j$ maximizing $$\sum_{i\in I}\sum_{j\in J}A_{ij}\min\left(x_i,B_{ij}y_j\right)\tag1$$ subject to $$\sum_{i\...

**0**

votes

**0**answers

48 views

### lyapunov stability for observer in dynamical system

I would like to use a stability analysis for the following problem:
Having a system discrete time
$$
\mathbf{x}(k+1) = \mathbf{Ax}(k) + \mathbf{B}\,\left(\mathbf{u}(k) + \mathbf{\widehat{z}^*}(k)\...

**1**

vote

**0**answers

129 views

### Solution to a Strongly Convex Non-smooth Minimization Problem involving an L1 Norm

Let $X \in \mathbb{R}^{n \times d}, w \in \mathbb{R}^d, y \in \{\pm 1\}^{n}, \alpha \in [0,1], \lambda \in \mathbb{R}$. I have an expression that looks as follows
$\frac{1}{2}\|Xw -y \|_{2}^2 + \...

**3**

votes

**2**answers

58 views

### Optimal covering of line subsegments using a given set of disks

Is there a way of picking a minimal set of disks that's still covering the same line subsegments as all the disks together? Any help or references highly appreciated. Below is just an illustrative ...

**1**

vote

**0**answers

31 views

### Is the integral functional $I(x) = \int_{0}^{T} \Lambda (t , x(t), \dot{x} (t)) \; dt $ lipschitz around $x_0$?

Let the function $\Lambda : [0,T] \times \mathbb{R^n} \times \mathbb{R^n} \to \mathbb R$ be continuously differentiable. Assume the integral functional $I(x) = \int_{0}^{T} \Lambda (t , x(t), \dot{x} (...

**5**

votes

**1**answer

35 views

### Optimization with weaker oracle than projection

I'm looking to solve the optimization problem
$$
min_{x \in C} ~ f(x),
$$
where $C \subset R^n$ is a closed, convex, bounded set and $f : R^n \to R$ a Lipschitz differentiable (nonconvex) function.
...

**1**

vote

**1**answer

73 views

### Maximize a Lebesgue integral subject to an equality constraint

I want to maximize $$\Phi_g(w):=\sum_{i\in I}\sum_{j\in I}\int\lambda({\rm d}x)\int\lambda({\rm d}y)\left(w_i(x)p(x)q_j(y)\wedge w_j(y)p(y)q_i(x)\right)\sigma_{ij}(x,y)|g(x)-g(y)|^2$$ over all choices ...

**2**

votes

**0**answers

35 views

### State-of-the-Art algorithms for bilevel optimization

I want to numerically solve a bilevel optimization problem of the form
$$ \min_y f(y, \hat x(y)), \qquad \hat x(y) = \arg\min_x g(x, y) $$
(for simplicity assume that $\min_x g(x, y)$ exists and is ...

**2**

votes

**2**answers

136 views

### Reference request on Min-Max theorem

Consider the following min-max problem
$$\inf_{x\in M} \sup_{y\in N} F(x,y),$$
where $F: M\times N\to\mathbb R$ is Lipschitz and $y\mapsto F(x,y)$ is concave for all $x\in M$. Could we derive $\...

**0**

votes

**1**answer

43 views

### Variant of the linear programming problem

Good afternoon, my experience in mathematical programming is low. I would like to know if there is any general method to address the following problem:
$$\text{Minimize }\sum_{i=1}^n d_i(x_j)$$
$$s.a....

**3**

votes

**0**answers

187 views

### Maximize an $L^p$-functional subject to a set of constraints

Let
$(E,\mathcal E,\lambda)$ and $(E',\mathcal E',\lambda')$ be measure spaces
$f\in L^2(\lambda)$
$I$ be a finite nonempty set
$\varphi_i:E'\to E$ be bijective $(\mathcal E',\mathcal E)$-measurable ...