Write down the Linear Program (LP) relaxation of an IP Plot the graphical representation of an IP and find the optimal solution Understand the relationship between optimal solution of an IP and the ...

$$ \begin{array}{ll} \underset{x \in \mathbb{R}^n}{\min} \quad & \langle c, x \rangle \\ \text{s.t.} \quad & L \leq A x \leq U, \\ & l \leq x \leq u . \end{array ...

Abstract: Fractional programming (FP) is a branch of mathematical optimization that deals with the optimization of ratios. It is an invaluable tool for signal processing and machine learning, because ...

Professional mathematicians have been stunned by the progress amateurs have made in solving long-standing problems with the ...

Tessellations aren’t just eye-catching patterns—they can be used to crack complex mathematical problems. By repeatedly reflecting shapes to tile a surface, researchers uncovered a method that links ...

Top 50 CBSE Class 12 Maths MCQs with Answers: CBSE Class 12 Mathematics Exam 2026 is scheduled to be held on 09 March 2026 ...

AS coding becomes an increasingly important skill for students to learn from a young age, schoolmates Chin Ling Yan and V. Priyangka, both 15, are eager to stay in the loop. “This is completely ...

Software engineering is the branch of computer science that deals with the design, development, testing, and maintenance of software applications. Software engineers apply engineering principles and ...

Abstract: Go beyond the basics with this in-depth guide to quantum programming. Here’s something you already know: quantum computing is a deep subject. Quantum Programming in Depth takes you beyond ...

This repository provides a solution to the standard Capacitated Vehicle Routing Problem with Time Windows (CVRPTW). In a CVRPTW, we aim to optimize the routes of a fleet of vehicles serving customers ...