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

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

971 questions
Filter by
Sorted by
Tagged with
95 views

70 views

### Is there a specific name for this optimization problem?

Let $A$ be an $n\times n$ symmetric positive definite matrix with eigenvalues and eigenvectors $\lambda_1\ge\lambda_2\ge\cdots\ge\lambda_n>0$ and $v_1,v_2,\cdots,v_n$ respectively. We know that the ...
53 views

### Lagrangian multipliers and a variant of Newton's method

A variant of Newton's method for solving the equality constrained problem $$\begin{array}{ll} \min &f(x) \\ \text{s.t.} & h(x) = 0 \end{array}$$ is as follows: \...
35 views

### Deployment and dispersion in triangular regions

Definitions (from C. Stanley Ogilvy's 'Tomorrow's Math'): Deployment: To place a specified number $n$ of points (stations) in a region such that the maximum distance of any point in the region from ...
30 views

### Karush-Kuhn-Tucker in discrete time dynamic optimization

I need to solve the following problem: $\max_{p_t\in [\phi_1(s_t),\phi_2(s_t)]} \sum_{t=0}^\infty p_t\times(a+\alpha s_t-p_t)$, subject to $s_0$ given and $s_{t+1}=\beta(s_t+\eta(a+\alpha s_t-p_t))$. ...
25 views

65 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) ...
89 views

### Best approximation of piecewise constant function by Lipschitz functions

Let $f=\sum_{n=1}^N k_n I_{E_n}$ where $E_n$ are Borel subsets of $\mathbb{R}^n$ and $k_n\in \mathbb{R}^m$ with non-negative entries, and let $\mu$ be a finite Borel measure on $\mathbb{R}^n$. What ...
107 views

### Maximizing a piecewise-linear convex function

Crossposted on Operations Research SE. I am working on an optimization problem where some of the terms of the objective function to maximize are expressed as a piecewise linear function of variables: ...
34 views

### Relation of 1-trees to optimal tours

Question: given a complete symmetric graph $G(V,E)$ with $n$ vertices and edges $e_{ij}$ having weight $\omega_{ij}$, does there always exists a vector of vertex potentials $(\pi_1,\,\dots,\,\pi_n)$ ...
25 views

83 views

### Bounds on minimum solutions to empirical and theoretical objective functions

Let $P$ and $Q$ be two probability distributions and let $$S_0 = \min_{f,g} \left[ \int f(x)\, dP(x) + \int g(y)\, dQ(y) \right]$$ such that $f(x)+g(y) \geq \langle{x,y\rangle}$ where $f,g$ are ...
92 views

### Strongly convex optimization error bounds

Suppose I want to minimize a function $G(f)$ using first order strongly convex methods and I get a solution $f^*$, where we restrict our solution set to strongly convex $f$. Now let $f_0$ be the ...
100 views

Let $(M,g,m_0)$ be a pointed-Hadamard manifold with Riemmanian distance function $d_g$, $(X,\Sigma,\mu)$ be a finite measure space. We use $L^2(\mu;M,m_0)$ to denote the metric space consisting of ...
29 views

### Complexity of calculating the optimal amalgamation of an optimal cycle-cover

Let $G(V,E)$ be a complete symmetric graph with positive edge weights and let further $\mathcal{C}=\lbrace C_1,\,\cdots\,C_k\rbrace$ be the minimum-weight vertex-disjoint cycle cover. The set $E$ of ...
227 views

### Signed distance function and level set

For $\phi\in C^1(\mathbb{R}^N)$ with $$\omega_{\phi}=\{x\in\mathbb{R}^N\ |\ \phi(x)>0\}$$ being a bounded set with \$\nabla\phi (x)\neq 0,\ \forall\ x\in\phi^{-1}(0)=\partial\omega_{\phi}\neq \...
81 views

### Normal cones and KKT conditions

I'm trying to understand a statement from the book "Perturbation Analysis of Optimization Problems", by Bonnans and Shapiro. Let me start by providing some context. In page 148, the authors ...