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

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

1,025 questions
Filter by
Sorted by
Tagged with
82 views

### Relegation of Farkas' fundamental theorem to a lemma

Farkas proved his famous result (which, nowadays, is fundamental in optimization theory) in 1902 and called it Grundsatz der einfachen Ungleichung which may be translated as fundamental theorem of ...
1 vote
36 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 ...
1 vote
37 views

1 vote
142 views

### Can we substitute this KKT condition into this optimization problem to reformulate the optimization problem?

Suppose I have the following optimization problem $$\min\limits_{\mathbf{x},\mathbf{y}} f(\mathbf{x},\mathbf{y}) \tag{1}$$ It is already known that the target function $f$ is continuous and ...
60 views

### Sum-of-guesses-minimization problem (also does this problem already exist in the literature)?

Inspired by some recent real-world situations, I thought of this problem: An adversary has selected a positive real number $p \ge 1$ not known to you. You have to pick numbers $x_1, x_2, \dots$ in ...
1 vote
23 views

### Non-differentiability of the set of optima of certain optimization problems

Let $X \subseteq \mathbb{R}^n$ be compact and say the function $f \colon X \to \mathbb{R}$ is locally Lipschitz continuous. Say $\mathcal{X}$ is the set of all solutions of the following optimization ...
70 views

12 views

### Convergence of solutions of regularised least square problems

Let $\mathcal{H}_1$ and $\mathcal{H}_2$ be two Hilbert spaces ($\mathcal{H_2}$ being finite dimensional, but I don't think that it matters). Consider $(A_{\lambda})_{\lambda>0}$ a familly of ...
51 views

1 vote
232 views

### Optimization of a integral function

I have a function $h(y,x_1,x_2,\ldots,x_n)$. It is known that the minimum value of $h$ for any $y$ is attained when $x_1 = x_n$ and $x_2 = x_3 = \cdots = x_{n-1}$. Now consider the following function \...
54 views

93 views

127 views

### Minimizing quadratic objective under orthogonality constraints

The following problem is motivated from Generalized Procrustes Analysis. I am wondering if it is possible to obtain a closed form minimizer (which may involve SVD or some other decomposition of a ...
44 views

### A variant of the elliptope relaxation

Given a p.s.d. matrix $A$, one may want to find: $$\max_x x^t A x \mbox{ such that } x \mbox{ has entries }1 \mbox{ or } {-1}.$$ This hard problem has a well known relaxation based on the so called ...
74 views

As we all know, a classic optimization problem can be represented in the following way: Given a function $f: A \to \mathbb{R}$, find an element $x_0 \in A$ such that $f(x_0) \le f(x)$ for all $x \in ... 0 votes 0 answers 66 views ### On least-squares with positive semidefinite constraints Given real symmetric matrix$\mathbf{R} \in \mathbb{S}^{n\times n}$and matrices$\mathbf{X}_n, \mathbf{X}_{n-1} \in \mathbb{R}^{n \times m}, \begin{array}{ll} \underset{\mathbf{A} \in \mathbb{R}^{... 1 vote 2 answers 135 views ### Partitioning unit square with equal frequency rectangles If I had to partition the unit square [0,1]\times[0,1] into k^2 rectangles such that the sum of their diagonals is minimum possible, I would simply choose the k \times k grid of squares. Now ... 0 votes 0 answers 39 views ### Simplest sensitivity analysis in semi-infinite linear programming Consider a standard linear program of the form \begin{align*} \min_{x}c^{\top}x & \,\,\text{subject to}\\ Ax & =b\\ b & \geq0\,. \end{align*} It is well-known that if we perturb the right-... 16 votes 2 answers 735 views ### What tools should I use for this problem? Suppose we have d cylindrical metal bars, with radius l, attached orthogonal to a support in random places: Now we have to attach bars with radius k EVENLY SPACED, with distance p between ... 0 votes 0 answers 29 views ### What's "Arrow-Hurwicz method" for solving saddle point optimization problems? I have seen some papers on convex-concave optimization citing the "Arrow-Hurwicz method" from the paper  in different ways. However, since I cannot find a pdf version of this paper and ... 3 votes 0 answers 65 views ### Projection onto level set of convex functional Fix a probability space (\Omega,\mathcal{F},\mathbb{P}) and let F:L^2_{\mathbb{P}}(\mathcal{F})\rightarrow (-\infty,\infty] be bounded-blow, convex, lower semi-continuous, and not identically ... 0 votes 0 answers 73 views ### Why is Gaussian distribution always chosen for smoothed analysis? I came across the algorithmic perfomance analysis model of smoothed analysis. In all references that I read a Gaussian distribution was used for perturbation (e.g. Spielman and Teng 2004 for the ... 2 votes 1 answer 90 views ### Minimization of an entropy type functional with biased expectation constraint This question is a continuation of Minimization of an entropy type functional Let \mathcal P_c be the set of probability densities on [0,1] with mean c\in [0,1], i.e. p\in \mathcal P_c iff\... 3 votes 1 answer 123 views ### Minimization of an entropy type functional Let\mathcal P$be the set of probability densities on$[0,1]$with mean$1/2$, i.e.$p\in \mathcal P$iff$$\int_0^1 p(x)dx=1,\quad \int_0^1 xp(x)dx=\frac{1}{2}\quad \mbox{and}\quad p(x)\ge 0, ~~\... 0 votes 0 answers 87 views ### Optimization problem where the objective function returns a function instead of a real number As we all know, a classic optimization problem can be represented in the following way: Given: a function$f: A \rightarrow \mathbb{R}$from some set$A$to the real numbers Sought: an element$x_0 ∈ ...
On page 43 of Nocedal & Wright's Numerical Optimization, the authors provide the following Theorem 3.4 without any proof: Suppose that $f:\mathbb{R}^n\rightarrow \mathbb{R}$ is twice continuously ...
To recall Arrow's theorem: Suppose we have a finite set $X$ of voters and a finite set $Y$ of candidates. An election is a map $\phi: X \rightarrow T$ where $T$ is the space of total orderings of $Y$. ...