optimization

The n queens problem is to place on an n × n chessboard n queens so that none attacks any other. This means there is only one queen on every horizontal, vertical, and diagonal line. When n is a prime number ≥ 5, it is sufficient to place the queens on a line that has slope 2, 3, 4, …, […] The post Queens on a prime order board first appeared on John D. Cook .

One variant of the traditional sphere packing problem in $\mathbb R^3$ asks what the density $\rho_r$ of spheres of equal radii $r$ one can fit in a unit cube without exceeding the boundary ...

I'm curious about an exercise found in Optimization Methods in Finance . Exercise 8.2 (pg 143) explores a variant of the more commonly used form of MVO. When I refer to the more common variant I'm talking about: $$ \begin{aligned} \operatorname{max}_x \mu^Tx - \frac{\delta}{2}x^T\Sigma x & \\ Ax &= b \\ Cx &\ge d \end{aligned} $$ The variant that directly uses standard deviation by taking the squ…

When trying to design asymmetric smooth-step functions $f_{\lbrack 0,1\rbrack}(x)$ that for $0<a<1$ satisfy: $f(0)=0,\ f'(0)=0,\kappa\lbrack f\rbrack(0)=0$ $\kappa\lbrack f\rbrack(a)=0$ ...

Scientific Reports, Published online: 29 June 2026; doi:10.1038/s41598-026-58314-3 Machine learning prediction and hybrid GRA–AHP optimization of AWJM parameters of ultrasonic assisted stir cast Al6061–B$$_4$$C–ZrO$$_2$$ composites

I came across this problem in Facebook. What is the limit of the definite integral $$\int\limits_{x^2+y^2\le R^2}\frac{2 x^2+1}{x^4+6 x^2 y^2+y^4+1}-\frac{y^2+1}{x^4+y^4+2} \,dx dy $$ as $R\to\infty$? ...

Let the initial triple be $(a_1, a_2, a_3) = (1, 3, 4)$, or equivalently the multiset $S_0 = \{1, 3, 4\}$. Define an operation as follows: Choose two distinct instances $x, y$ from $S$ (their values ...

Cocktail Optimization, an Integer Programming Problem June 18, 2026 I’ve been interested in integer programming problems for a long time (they the most interesting problems in dedupe). In the past, I approached them by writing custom branch-and-bound algorithms. I have been using Google’s OR Tools for a project that involves a lot of vehicle routing, and I started to wonder how these mixed intege…

Why production-level AI optimization modeling agent needs reproducibility and portability, and how IR helps achieve them The post The Secret to Reproducible and Portable Optimization: ORPilot’s Intermediate Representation (IR) appeared first on Towards Data Science .

constructive mathematics, realizability, computability propositions as types, proofs as programs, computational trinitarianism Wikipedia defines control theory as a field of control engineering and applied mathematics that deals with the control of dynamical systems Michel Fliess, Jean Lévine, Philippe Martin, Pierre Rouchon, Flatness and defect of non-linear systems: introductory theory and exam…

Scientific Reports, Published online: 17 June 2026; doi:10.1038/s41598-026-57702-z Quantum-inspired hybrid optimization framework for energy-efficient clustering and routing in wireless sensor networks

A simple linear problem goes min c'x such that f_i(x)<= 0 and Ax=b x Suppose we make all constraints affine. Then Dx-e<=0 and Ax-b =0 We get the Langrangian function as c'x + λ'(Dx-e) +ν'(Ax-b) and since Ax-b is 0, we reduce L to c'x + λ'(Dx-e) The dual function g is inf L(x,λ) x Then I... Read more

Discover the latest enhancements in Simcenter Flux 2026.1, including accelerated electromagnetic simulations, improved modeling productivity, expanded engineering workflow connectivity and emerging approaches leveraging surrogate models and optimization.

Mathematicians have considered how to watch every corner of a space—but soccer adds moving players, blocked views and constant action

Scientific Reports, Published online: 11 June 2026; doi:10.1038/s41598-026-54224-6 Multi-objective optimization of low-noise pervious concrete using a stacking ensemble learning and NSGA-II approach

A new neural field-based optimization method aims to reshape parts to reduce overhangs and, in turn, minimize the need for 3D printing support structures. The post Neural Shape Optimization Could Cut 3D Print Supports appeared on Fabbaloo .

Below is an open problem, an approachable problem, one perhaps you will be the one to solve! We send a bit over a noisy grid, starting from the origin and propagating out as a wave. Can we recover the original bit when looking at just the wavefront? This is easy to solve for 1D, mostly solved in 2D, and still open in 3D and above. Here is the lecture that introduced the problem to me, as well as …

From ThreadPoolExecutor to httpx AsyncClient: True Async Refactoring Published on : 2026-06-06 Reading time : 6 min Tags : #python #async #performance #optimization The Problem: Fake Async The supabase-async library claimed to be async but actually wrapped synchronous calls with ThreadPoolExecutor: # ❌ Fake async (old code) class SupabaseAsync : def __init__ ( self ): self . _executor = ThreadPoo…

Scientific Reports, Published online: 07 June 2026; doi:10.1038/s41598-026-56529-y A novel hybrid intelligent optimization strategy for multi-objective trajectory planning of robotic arms in precision assembly scenarios