COSMO: A Conic Operator Splitting Method for Convex Conic Problems

Global Error Bounds for Convex Conic Problems

This paper aims at deriving and proving some Lipschitzian type error bounds for convex conic problems in a simple way First it is shown that if the recession directions satisfy Slater s condition then a global Lipschitzian type error bound holds Alternatively if the feasible region is bounded then the ordinary Slater condition guarantees a global Lipschitzian type error bound These can be consi...

Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding

We introduce a first-order method for solving very large convex cone programs. Themethod uses an operator splittingmethod, the alternating directionsmethod of multipliers, to solve the homogeneous self-dual embedding, an equivalent feasibility problem involving finding a nonzero point in the intersection of a subspace and a cone. This approach has several favorable properties. Compared to inter...

Conic Structure of the Non-negative Operator Convex Functions

The conic structure of the convex cone of non-negative operator convex functions on (0,∞) (also on (−1, 1)) is clarified. We completely determine the extreme rays, the closed faces, and the simplicial closed faces of this convex cone.

-Duality Theorems for Convex Semidefinite Optimization Problems with Conic Constraints

An Augmented Lagrangian Method for Conic Convex Programming

We propose a new first-order augmented Lagrangian algorithm ALCC for solving convex conic programs of the form min { ρ(x) + γ(x) : Ax− b ∈ K, x ∈ χ } , where ρ : Rn → R ∪ {+∞}, γ : Rn → R are closed, convex functions, and γ has a Lipschitz continuous gradient, A ∈ Rm×n, K ⊂ Rm is a closed convex cone, and χ ⊂ dom(ρ) is a “simple” convex compact set such that optimization problems of the form mi...