Web Reference: start with nonconvex problem: minimize h(x) subject to x ∈ C find convex function ˆh with ˆh(x) ≤ h(x) for all x ∈ dom h (i.e., a pointwise lower bound on h) find set ˆC ⊇ C (e.g., ˆC = conv C) described by linear equalities and convex inequalities CVX implements disciplined convex programming in Matlab transforms user-specified convex programs into standard form passes standard-form problems to solvers interprets solver exit status (solved, infeasible, unbounded, . . . In this lecture, we will go over a number of classes of convex optimization problems, including linear programs, quadratic programs, second-order cone programs, and geometric programs.
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Last Updated: April 8, 2026
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