ISYE 6501 STUDY GUIDE 2026 FULL
CONTENT QUESTIONS AND ANSWERS
COMPLETE SET
◉ Optimization Problems - Network Optimization
Answer: Linear model on a graph (flow, shortest path, assignment) -
Fastest
◉ Optimization Problems - Linear Program (LP)
Answer: Linear Objective + Linear constraints, continuous variables
◉ Optimization Problems - Convex Quadratic Programs
Answer: Quadratic Convex Objective + Linear constraints
◉ Optimization Problems - Convex Optimization
Answer: Convex objective + convex constraint set
◉ Optimization Problems - Integer Program
Answer: LP but some/all variables must be integers
◉ Optimization Problems - Binary Program
,Answer: IP where variables are 0/1 only
◉ Optimization Problems - General Non-Convex
Answer: Non-convex objective or constraints
◉ Optimization - Two-step Structure
Answer: Initialize: Create a starting solution
Iterate: Repeat until convergence
a. finding an improving direction t
b. choose a step size theta
c. update x_new = x_old _ theta*t
◉ Stochastic Optimization
Answer: Optimization when not all inputs are known exactly
◉ Stochastic Optimization Approaches
Answer: Conservative Constraints
Scenario Modeling
Dynamic Programming
◉ Stochastic Optimization - Conservative Constraints
Answer: Replacing an exact demand constraint with:
, x >= expected value + theta: ensures x will always be greater than
value
OR p(x >= value) >= p: finding the probability that x will be greater
than or equal to value
◉ Stochastic Optimization - Scenario Modeling
Answer: Define scenarios for multiple outcomes, then define
constraints and costs for each scenario
◉ Stochastic Optimization - Dynamic Programming
Answer: Systems are divided into states, at each state, a decision is
made and the system transitions to the next state
◉ Stochastic Optimization - Dynamic Programming Models
Answer: Deterministic Decision Process
Stochastic Decision Process
Markov Decision Process
Approximate Decision Process
◉ Non-Parametric Statistical Tests
Answer: Tests that do not assume a known underlying distribution -
work on ranking between values or binary outcomes rather than
exact values
CONTENT QUESTIONS AND ANSWERS
COMPLETE SET
◉ Optimization Problems - Network Optimization
Answer: Linear model on a graph (flow, shortest path, assignment) -
Fastest
◉ Optimization Problems - Linear Program (LP)
Answer: Linear Objective + Linear constraints, continuous variables
◉ Optimization Problems - Convex Quadratic Programs
Answer: Quadratic Convex Objective + Linear constraints
◉ Optimization Problems - Convex Optimization
Answer: Convex objective + convex constraint set
◉ Optimization Problems - Integer Program
Answer: LP but some/all variables must be integers
◉ Optimization Problems - Binary Program
,Answer: IP where variables are 0/1 only
◉ Optimization Problems - General Non-Convex
Answer: Non-convex objective or constraints
◉ Optimization - Two-step Structure
Answer: Initialize: Create a starting solution
Iterate: Repeat until convergence
a. finding an improving direction t
b. choose a step size theta
c. update x_new = x_old _ theta*t
◉ Stochastic Optimization
Answer: Optimization when not all inputs are known exactly
◉ Stochastic Optimization Approaches
Answer: Conservative Constraints
Scenario Modeling
Dynamic Programming
◉ Stochastic Optimization - Conservative Constraints
Answer: Replacing an exact demand constraint with:
, x >= expected value + theta: ensures x will always be greater than
value
OR p(x >= value) >= p: finding the probability that x will be greater
than or equal to value
◉ Stochastic Optimization - Scenario Modeling
Answer: Define scenarios for multiple outcomes, then define
constraints and costs for each scenario
◉ Stochastic Optimization - Dynamic Programming
Answer: Systems are divided into states, at each state, a decision is
made and the system transitions to the next state
◉ Stochastic Optimization - Dynamic Programming Models
Answer: Deterministic Decision Process
Stochastic Decision Process
Markov Decision Process
Approximate Decision Process
◉ Non-Parametric Statistical Tests
Answer: Tests that do not assume a known underlying distribution -
work on ranking between values or binary outcomes rather than
exact values
