Graph Implementations for Nonsmooth Convex Programs
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Citations
Spectrally efficient multicarrier communication systems:signal detection, mathematical modelling and optimisation
Joint Metering and Conflic t Resolution in Air Traffic C ontrol
Solution Refinement at Regular Points of Conic Problems
A geometric analysis of convex demixing
Stationary-sparse causality network learning
References
Convex Optimization
YALMIP : a toolbox for modeling and optimization in MATLAB
Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
Linear Programming and Extensions
Related Papers (5)
Frequently Asked Questions (9)
Q2. What contributions have the authors mentioned in the paper "Graph implementations for nonsmooth convex programs" ?
The transformation approach dates back to the very first days of linear programing and is usually taught as a collection of tricks that a modeler can use to reformulate problems by hand this paper.
Q3. What is the definition of convex programming?
It consists of two key components:9 an atom library--a collection of functions or sets with known properties of curvature (convexity and concavity) and monotonicity; and 9 the DCP ruleset--a finite enumeration of ways in which atoms may be combined in objectives and constraints while preserving convexity.
Q4. What are the key omissions in the graph?
Key omissions include logarithms, exponentials, and entropy; such functions simply cannot be exactly represented in an SQLP solver.
Q5. What is the function de t_ inv?
The function de t_ inv represents faet_inv('), including the implicit constraint that its argument be symmetric and positive definite.
Q6. What is the exact transformation of the Huber penalty?
Note that the precise transformation depends on how square and abs are themselves implemented; multilevel transformations like this are quite typical.
Q7. What is the definition of a valid const ra in t?
A valid const ra in t is - a set membersh ip relat ion (E) in which the lef t-hand side (LHS) is affineand the r igh t -hand side (RHS) is a convex set.- an equali ty (=) with an affine LHS and an affine RHS.
Q8. what is the fundamental principle of convex analysis?
4.1 T h e BasicsRecall the definition of the epigraph of a function f : R n --~ (R U +oc):epi f _a { (x, y) e R n x a The authorf (x) _ y }. (11)A fundamental principle of convex analysis states that f is a convex function if and only if epi f is a convex set.
Q9. what is the cvx a t o m funct ?
So if x is a real variable, thensquare( x )is accepted by cvx; and, thanks to the above rule, so issquare( A 9 x + b )if A and b are cons tan t matr ices of compat ib le size.