ISYE 6669 / ISYE6669 Midterm Exam (Latest Update 2025 / 2026) Deterministic Optimization | Questions & Answers | Grade A | 100% Correct - Georgia Tech

ISYE 6669 / ISYE 6669 Midterm
Exam (Latest Update )
Deterministic Optimization |
Questions & Answers | Grade A |
100% Correct - Georgia Tech


Question:
Points and Vectors
Answer:
Algebraically, a point in 𝑛-dimensional space is given by its
coordinates: 𝒙 = (𝑥1,..., 𝑥n)^T ∈ R^n


In this way, a point is also called a vector




Question:
Ray
Answer:
Consists of a starting point 𝑎 and all the points in a direction 𝑑

,Question:
Line
Answer:
A line consists of two rays starting at a point pointing two opposite directions




Question:
Plane
Answer:
a plane in 𝑅^n is the set of solutions of one linear equation in 𝑛 variables: 𝑎1𝑥1
+ ⋯+ 𝑎n𝑥n = 𝑐




Question:
Halfspace
Answer:
Half the whole space represented by:
𝑎1𝑥1 + ⋯+ 𝑎n𝑥n <= 𝑐
𝑎1𝑥1 + ⋯+ 𝑎n𝑥n >= 𝑐

, Question:
Polyhedron
Answer:
A polyhedron is the intersection of a finite number of halfspaces


Corner points are responsible for creating the set




Question:
Convex Combination of Two Points
Answer:
Given two points 𝒂, 𝒃 ∈ 𝑅^n, a convex combination of 𝒂, 𝒃 is given by 𝒙 = 𝜆𝒂
+ (1 − 𝜆) 𝒃




Question:
Extreme Point
Answer:
A point 𝒙 in a polyhedron 𝑃 is an extreme point if and only if 𝒙 is not a convex
combination of other two different points in 𝑃.


Extreme points are "corner points".