Mixed-Integer Quadratic Programming for Beginners
Learn Mixed-Integer Quadratic Programming (MIQP) visually and intuitively!
This video builds from quadratic programming (QP) to mixed-integer quadratic programming (MIQP), showing step by step how restricting a variable to integers — and adding a cross term to the objective — reshapes the optimal solution.
What's covered:
• Quadratic programming recap: maximizing 9x² + y² over a feasible polygon
• How binary integer constraints collapse the feasible region to discrete line segments
• Why the MIQP optimal (x=0, y=9) differs from the continuous QP optimal (x=3, y=4.5)
• The effect of adding a cross term 4xy: tilted ellipses and a new optimal (x=1, y=7.5)
• Side-by-side comparison of different objectives → different optimal solutions
Perfect for students in operations research, machine learning, or anyone curious about optimization.
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