kkt-conditions #

Visualizes KKT for an inequality-constrained optimization: a point x moves toward the feasible set (inside a circle). The left panel shows the feasible region and vectors for -∇f (unconstrained descent), μ∇g (constraint push), and the stationarity residual ∇f+μ∇g shrinking near the solution. The right panel is a live KKT checklist with gauges for primal feasibility g(x)≤0, multiplier μ≥0, and complementary slackness μ·g(x)=0.

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

01.Checking optimality conditions in constrained ML/regularized problems (e.g., SVM, L1/L2 constraints)
02.Deriving dual problems and interpreting multipliers (shadow prices) in operations research
03.Implementing/understanding constrained solvers (SQP, interior-point) and diagnosing active constraints

technical notes #

Uses a simple 2D toy problem with one inequality constraint g(x)=x1^2+x2^2−1≤0. The animated point follows a preset path and is smoothly projected to the boundary when outside to illustrate feasibility. μ is computed each frame via least-squares stationarity μ* = −(∇f·∇g)/||∇g||^2 clamped to μ≥0; complementary slackness is shown as the product μ·g(x). All drawing is grid-snapped for a blocky aesthetic and scales with canvas size.

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