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      Questions tagged [oc.optimization-and-control]

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

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      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\...
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      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 ...
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      1answer
      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 ...
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      0answers
      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 $...
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      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
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      0answers
      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
      0answers
      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
      2answers
      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
      0answers
      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} (...
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      votes
      1answer
      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
      1answer
      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
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      0answers
      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
      2answers
      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
      1answer
      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
      0answers
      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 ...

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