MML-13-06: Strong Duality, Slater's Condition & The Duality Gap – Practice Quiz

35 worked single-select and multiselect questions on Strong Duality, Slater's Condition & The Duality Gap. Cognitive level: Tier 2–4. Prerequisites: QS 13.5.

Develop conceptual understanding, step-by-step computations, ML diagnostics and the assigned theoretical derivations. Each explanation analyzes every choice by its content.

Learning objectives: Distinguish equality of optimal values from attainment and uniqueness. Check basic and refined Slater qualifications on explicit feasible sets. Calculate primal-dual gaps and certified suboptimality bounds. Solve primal and dual scalar or separable convex examples. Use KKT sufficiency with correct convexity and domain assumptions. Analyze failed qualifications, nonattainment and misleading solver certificates. Derive primal-dual identities and counterexamples.

Study references: Boyd & Vandenberghe, Convex Optimization, Sections 5.2.3 and 5.5.1–5.5.3.