| CCA (Computational Convex Analysis) |

CCA (Computational Convex Analysis) >> CCA (Computational Convex Analysis)

### CCA (Computational Convex Analysis)

- CCA — Computational Convex Analysis toolbox description
- gph
  - 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 — 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
- miscellaneous
  - common_version — Miscellaneous routines, library version
  - gph_version — Graph-Matrix Calculus (GPH), library version
  - lft_version — Legendre-Fenchel transform, library version
  - me_version — Moreau envelope, library version
  - op_version — Finite operator algorithms (OP), library version
  - plot_version — Function visualization routines, library version
  - plq_version — Piecewise linear quadratic (plq), library version
- op
  - 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.
- opt
  - 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
  - _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
  - pl_bb — Lower convex envelope/convex hull, Beneath-Beyond algorithm
  - 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_generic — Generic Legendre Fenchel Transform (LFT)
  - 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
  - pl_ll — The Lasry-Lions double envelope approximation
  - 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_generic — Generic Moreau envelope
  - 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 — Parametric Moreau Envelope, PME algorithm
  - pl_ph_direct — Discrete Pasch-Hausdorff envelope
- plq
  - _plq_conv_on_interval — Piecewise linear quadratic (plq), two-piece convexity on interval
  - 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 — Piecewise linear 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

| CCA (Computational Convex Analysis) |