Solving the Optimization Problem
{"Image DocumentName": "Solving the Optimization Problem", "Image ImageDescription": "Find w and b such that. \u03a6(w) =\u00bd wTw is minimized; and for all {(xi ,yi)}: yi (wTxi + b) \u2265 1. Need to optimize a quadratic function subject to linear constraints. Quadratic optimization problems are a well-known class of mathematical programming problems, and many (rather intricate) algorithms exist for solving them. The solution involves constructing a dual problem where a Lagrange multiplier \u03b1i is associated with every constraint in the primary problem: Find \u03b11\u2026\u03b1N such that. Q(\u03b1) =\u03a3\u03b1i - \u00bd\u03a3\u03a3\u03b1i\u03b1jyiyjxiTxj is maximized and. (1) \u03a3\u03b1iyi = 0. (2) \u03b1i \u2265 0 for all \u03b1i.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}