nmiPiano Class Reference

Implementation of nmiPiano (algorithm 4) as proposed in [1]: [1] P. Ochs, Y. Chen, T. Brox, T. Pock. iPiano: Inertial Proximal Algorithm for Nonconvex Optimization. SIAM J. Imaging Sciences, vol. 7, no. 2, 2014. More...

#include <nmipiano.h>

Inheritance diagram for nmiPiano:

Classes
struct	Iteration
	Structure representing an iteration, passed as is to a callback function to be able to monitor process. More...
struct	Options
	Options of algorithm. More...

Public Member Functions
	nmiPiano (const std::function< float(const Eigen::MatrixXf &)> f, const std::function< void(const Eigen::MatrixXf &, Eigen::MatrixXf &)> df, std::function< float(const Eigen::MatrixXf &)> g, const std::function< void(const Eigen::MatrixXf &, Eigen::MatrixXf &, float alpha)> prox_g, Options options, const std::function< void(const Iteration &)> callback=[](const Iteration &iteration) -> void{})
	Constructor. More...
	~nmiPiano ()
	Destructor.
void	optimize (Eigen::MatrixXf &x_star, float &f_x_star)
	Optimize the given objective using the nmiPiano algorithm. More...

Static Public Member Functions
static void	silent_callback (const Iteration &iteration)
	Silent callback to use with nmiPiano. More...
static void	default_callback (const Iteration &iteration, int n=10)
	Default callback to use with nmiPiano. More...
static void	brief_callback (const Iteration &iteration, int n=10)
	Brief callback to use with nmiPiano. More...
static void	file_callback (const Iteration &iteration, const std::string &file)
	File callback, used to write all information to the specified file. More...
static void	plot_callback (const Iteration &iteration, const std::string &file)
	File callback for plotting, writes CSV output of format: iteration,f,g,alpha_n,L_n,Delta_n. More...

Protected Member Functions
void	initialize (Iteration &iteration)
	Initialize the iteration structure (i.e. set iteration 0): More...
float	estimateL (const Iteration &iteration)
void	iterate (Iteration &iteration, float beta, Eigen::MatrixXf &x_np1)
	Do an iteration, i.e. compute x_np1. More...
bool	checkLipschitz (const Iteration &iteration, const Eigen::MatrixXf &x_np1)
	Check the lipschitz condition for backtracking. More...

Protected Attributes
std::function< float(const Eigen::MatrixXf &)>	f_
	The smooth part of the objective function.
std::function< void(const Eigen::MatrixXf &, Eigen::MatrixXf &)>	df_
	Gradient of smooth part of the objective function (i.e. derivative).
std::function< float(const Eigen::MatrixXf &)>	g_
	Convex, nonsmooth part of objective.
std::function< void(const Eigen::MatrixXf &, Eigen::MatrixXf &, float)>	prox_g_
	Proximal map for g, i.e. (I + alpha_n*g)^(-1).
std::function< void(const Iteration &)>	callback_
	Callback, can e.g. be sued to monitor process using the provided information in the Iteration structure.
Options	options_
	Options.

Detailed Description

Implementation of nmiPiano (algorithm 4) as proposed in [1]: [1] P. Ochs, Y. Chen, T. Brox, T. Pock. iPiano: Inertial Proximal Algorithm for Nonconvex Optimization. SIAM J. Imaging Sciences, vol. 7, no. 2, 2014.

Implementation of nmiPiano as described in [1] and [2]:

[1] P. Ochs, Y. Chen, T. Brox, T. Pock. iPiano: Inertial Proximal Algorithm for Nonconvex Optimization SIAM Journal of Imaging Sciences, colume 7, number 2, 2014. [2] D. Stutz. Seminar paper "iPiano: Inertial Proximal Algorithm for Non-Convex Optimization" https://github.com/davidstutz/seminar-ipiano

The code is published under the BSD 3-Clause:

Copyright (c) 2016, David Stutz All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Author

David Stutz

Constructor & Destructor Documentation

nmiPiano::nmiPiano	(	const std::function< float(const Eigen::MatrixXf &)>	f,
		const std::function< void(const Eigen::MatrixXf &, Eigen::MatrixXf &)>	df,
		std::function< float(const Eigen::MatrixXf &)>	g,
		const std::function< void(const Eigen::MatrixXf &, Eigen::MatrixXf &, float alpha)>	prox_g,
		Options	options,
		const std::function< void(const Iteration &)>	callback = [](const Iteration &iteration) -> void {  }
	)

Constructor.

Parameters

[in]	f
[in]	df
[in]	prox_g
[in]	callback

Member Function Documentation

void nmiPiano::brief_callback ( const Iteration &  iteration, int  n = 10  )

static

Brief callback to use with nmiPiano.

Parameters

[in]

iteration

bool nmiPiano::checkLipschitz ( const Iteration &  iteration, const Eigen::MatrixXf &  x_np1  )

protected

Check the lipschitz condition for backtracking.

Parameters

[in]	iteration
[in]	x_np1

Returns

void nmiPiano::default_callback ( const Iteration &  iteration, int  n = 10  )

static

Default callback to use with nmiPiano.

Parameters

[in]

iteration

void nmiPiano::file_callback ( const Iteration &  iteration, const std::string &  file  )

static

File callback, used to write all information to the specified file.

Parameters

[in]	iteration
[in]	file

void nmiPiano::initialize ( nmiPiano::Iteration &  iteration )

protected

Initialize the iteration structure (i.e. set iteration 0):

Parameters

[in]

iteration

void nmiPiano::iterate ( nmiPiano::Iteration &  iteration, float  beta, Eigen::MatrixXf &  x_np1  )

protected

Do an iteration, i.e. compute x_np1.

Parameters

[in]	iteration
[in]	beta
[out]	x_np1

void nmiPiano::optimize	(	Eigen::MatrixXf &	x_star,
		float &	f_x_star
	)

Optimize the given objective using the nmiPiano algorithm.

Parameters

[out]	x_star
[out]	f_x_star

void nmiPiano::plot_callback ( const Iteration &  iteration, const std::string &  file  )

static

File callback for plotting, writes CSV output of format: iteration,f,g,alpha_n,L_n,Delta_n.

Parameters

[in]	iteration
[in]	file

void nmiPiano::silent_callback ( const Iteration &  iteration )

static

Silent callback to use with nmiPiano.

Parameters

[in]

iteration

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The documentation for this class was generated from the following file:

• lib_ipiano/nmipiano.h