# Part I. CCA (Computational Convex Analysis)

Table of Contents

_pl_fusion — [Internal function] Merge 2 increasing sequences using classical programming; used to compute the Legendre-Fenchel conjugate.
_pl_fusionsci — [Internal function] Merge 2 increasing sequences using scilab syntax; used to compute the Legendre-Fenchel conjugate.
_pl_kaFeasiblePoint — Convex operators via optimization (OPT), Kernel average feasible point
_plq_conv_on_interval — Piecewise linear quadratic (plq), two-piece convexity on interval
CCA — Computational Convex Analysis toolbox description
pl_bb — Lower convex envelope/convex hull, Beneath-Beyond algorithm
common_version — Miscellaneous routines, library version
pl_lft_generic — Generic Legendre Fenchel Transform (LFT)
gph_add — Graph-matrix calculus (GPH), Addition of two functions
gph_eval — Graph-matrix calculus (GPH), Function evaluation
gph_function — Graph-matrix calculus (GPH), Function model
gph_isBounded — Graph-matrix calculus (GPH), Function domain bounded test
gph_isEqual — Graph-matrix calculus (GPH), Model equivalence test
gph_lft — Graph-matrix calculus (GPH), Legendre-Fenchel conjugate
gph_me — Graph-matrix calculus (GPH), Moreau envelope (Moreau-Yoshida approximate)
gph_pa — Graph-matrix calculus (GPH), Proximal Average (PA)
gph_plot — Graph-matrix calculus (GPH), Subdifferential plot
gph_plq< span c lass=" refpur pose"> ̵ 2; Convert a standard PLQ model to a Graph-Matrix Calculus (GPH) model.
gph_prox — Graph-matrix calculus (GPH), Proximal mapping
gph_scalar — Graph-matrix calculus (GPH), Function scalar multiplication
gph_version — Graph-Matrix Calculus (GPH), library version
pl_ll — The Lasry-Lions double envelope approximation
pl_lft_direct — [For comparison only] Legendre-Fenchel conjugate, direct computation
pl_lft_direct_2d — [For comparison only] 2D Legendre-Fenchel conjugate, direct computation
pl_lft_direct_d — [For comparison only] Legendre-Fenchel conjugate, direct computation on {1,...,n}
pl_lft_llt — Legendre-Fenchel conjugate, LLT algorithm
pl_lft_llt_2d — 2D Legendre-Fenchel conjugate, LLT algorithm
pl_lft_llt_3d — 3D Legendre-Fenchel conjugate, LLT algorithm
pl_lft_llt_d — Legendre-Fenchel conjugate, LLT algorithm on {1,...,n}
pl_lft_plt — Parametric Legendre Transform, PLT algorithm
lft_version — Legendre-Fenchel transform, library version
pl_me_brute_2d — [For comparison only] 2D Moreau envelope, brute force computation
pl_me_direct — [For comparison only] Moreau envelope, direct computation
pl_me_direct_2d — [For comparison only] 2D Moreau envelope, direct computation
pl_me_llt — Moreau envelope, LLT algorithm
pl_me_llt_2d — 2D Moreau envelope, LLT algorithm
pl_me_nep — Moreau envelope for convex functions, NEP algorithm
pl_me_nep_2d — 2D Moreau envelope for convex functions, NEP algorithm
pl_me_pe — Moreau envelope, Parabolic Envelope algorithm
pl_me_pe_2d — 2D Moreau envelope, PE algorithm
pl_me_plt — Par am etric Moreau E nvelope, PME a lgorithm
me_version — Moreau envelope, library version
pl_me_generic — Generic Moreau envelope
op_fitz — Evaluate the Fitzpatrick function of a given operator on a grid using the LLT2d algorithm.
op_fitz_brute — [For comparison only] Evaluate the Fitzpatrick function of a given operator on a grid.
op_fitz_direct — [For comparison only] Evaluate the Fitzpatrick function of a given operator on a grid.
op_fitzinf — Evaluate the Fitzpatrick function of infinite order of an operator on a grid using Rockafellar functions.
op_version — Finite operator algorithms (OP), library version
opt_co — Convex operators via optimization (OPT), Convex hull
opt_ic — Convex operators via optimization (OPT), Inf-convolution
opt_ka — Convex operators via optimization (OPT), Kernel average
opt_lft — Convex operators via optimization (OPT), Legendre-Fenchel transform (LFT)
opt_me — Convex operators via optimization (OPT), Moreau envelope
opt_pa — Convex operators via optimization (OPT), Proximal average
opt_version — Convex operators via optimization (OPT), library version
pl_ph_direct — Discrete Pasch-Hausdorff envelope
plot_version — Function visualization routines, library version
plq_add — Piecewise linear quadratic (plq), addition of two plq functions
plq_build — Piecewise linear quadratic (plq), build a zeroth- or first-order function approximation
plq_check — Piecewise linear quadratic (plq), Consistency check
plq_clean — Piecewise linear quadratic (plq), clears duplicate rows
plq_co — Piecewise linear quadratic (plq), Convex hull
plq_coDirect — Piecewise linear quadratic (plq), Convex hull (direct algorithm)
plq_coSplit — Piece wise l inear quadratic (plq), Convex hull (splitting algorithm)
plq_deconv_lft — Piecewise linear quadratic (plq), deconvolution (via LFT)
plq_diff — Piecewise linear quadratic (plq), function differentiation
plq_dom — Piecewise linear quadratic (plq), function effective domain
plq_eval — Piecewise linear quadratic (plq), evaluate a plq function on a grid
plq_fitzinf0 — Compute the PLQ Fitzpatrick function of infinite order of an operator on an (x,0) grid using Rockafellar functions.
plq_fitzinf0_direct — [For comparison only] Compute the PLQ Fitzpatrick function of infinite order of an operator on an (x,0) grid using Rockafellar functions.
plq_function — Piecewise linear quadratic (plq) function description
plq_gpa — Piecewise linear quadratic (plq), generalized proximal average
plq_gph — Convert a PLQ subdifferential model to a standard PLQ model.
plq_infconv_lft — Piecewise linear quadratic (plq), Inf-convolution (via LFT)
plq_isConvex — Piecewise linear quadratic (plq), convexity test
plq_isEqual — Piecewise linear quadratic (plq), Model equivalence test
plq_lft — Piecewise linear quadratic (plq), Legendre-Fenchel conjugate
plq_ll — Piecewise linear quadratic (plq), Lasry-Lions double envelope
plq_max — Piecewise linear quadratic (plq), Maximum function
plq_me — Piecewise linear quadratic (plq), Moreau envelope
plq_me_max_scale — Piecewise linear quadratic (plq), Maximum scale for Moreau envelope
plq_min — Piecewise linear quadratic (plq), Minimum function
plq_minPt — Piecewise linear quadratic (plq), minimum point
plq_pa — Piecewise linear quadratic (plq), convex proximal average via conjugates
plq_pa_mu — Piecewise linear quadratic (plq), nonconvex proximal average via Moreau envelopes
plq_plot — Piecewise linear quadratic (plq), plot function
plq_plotMultiple — Piecewise linear quadratic (plq), plot multiple functions
plq_plotpa — Piecewise linear quadratic (plq), plot convex proximal average
plq_plotpa_lambdaSet — Piecewise linear quadratic (plq), plot nonconvex proximal average over lambda
plq_plotpa_muSet — Piecewise linear quadratic (plq), plot nonconvex proximal average over the smoothing parameter mu
plq_proj — Piecewise linear quadratic (plq), projection of a (not necessarily convex) function on the set of plq (convex) functions
plq_rock — Compute the PLQ Rockafellar function R(A,a(k)) of an operator A.
plq_scalar — Piecewise linear quadratic (plq), multiply a plq function by a scalar
plq_version — Piecewise linear quadratic (plq), library version