Forces a constant multiplier on the descent direction chosen by the algorithm. This is meant to be used by the steepestdescent or conjugategradients solvers. To use this method, specify linesearch_constant as an option, and your chosen constant alpha > 0 in the problem structure, as follows: problem.linesearch = @(x, d) 1.0; % choose any positive real number options.linesearch = @linesearch_constant; x = steepestdescent(problem, [], options); The effective step (that is, the vector the optimization algorithm retracts) is constructed as alpha*d, and the step size is the norm of that vector. Thus: stepsize = alpha*norm_d. For steepestdescent, we have d = -grad f(x). The step is executed by retracting the vector alpha*d from the current point x, which gives newx (the returned point). This line-search method does not require any cost function evaluations, as there is effectively no search involved. Inputs problem : structure holding the description of the optimization problem x : current point on the manifold problem.M d : tangent vector at x (descent direction) storedb : StoreDB object (handle class: passed by reference) for caching storedb is optional. Outputs stepsize : norm of the vector retracted to reach newx from x. newx : next iterate using the constant stepsize, such that the retraction at x of the vector alpha*d reaches newx. newkey : key associated to newx in storedb lsstats : statistics about the line-search procedure (costevals, stepsize, alpha). See also: steepestdescent conjugategradients linesearch

- StoreDB
- canGetLinesearch Checks whether the problem structure can give a line-search a hint.
- getLinesearch Returns a hint for line-search algorithms.

0001 function [stepsize, newx, newkey, lsstats] = ... 0002 linesearch_constant(problem, x, d, ~, ~, ~, storedb, ~) 0003 % Forces a constant multiplier on the descent direction chosen by the algorithm. 0004 % 0005 % This is meant to be used by the steepestdescent or conjugategradients solvers. 0006 % To use this method, specify linesearch_constant as an option, and your chosen 0007 % constant alpha > 0 in the problem structure, as follows: 0008 % 0009 % problem.linesearch = @(x, d) 1.0; % choose any positive real number 0010 % options.linesearch = @linesearch_constant; 0011 % x = steepestdescent(problem, [], options); 0012 % 0013 % The effective step (that is, the vector the optimization algorithm retracts) 0014 % is constructed as alpha*d, and the step size is the norm of that vector. 0015 % Thus: stepsize = alpha*norm_d. 0016 % For steepestdescent, we have d = -grad f(x). 0017 % The step is executed by retracting the vector alpha*d from the current 0018 % point x, which gives newx (the returned point). 0019 % This line-search method does not require any cost function evaluations, 0020 % as there is effectively no search involved. 0021 % 0022 % Inputs 0023 % 0024 % problem : structure holding the description of the optimization problem 0025 % x : current point on the manifold problem.M 0026 % d : tangent vector at x (descent direction) 0027 % storedb : StoreDB object (handle class: passed by reference) for caching 0028 % 0029 % storedb is optional. 0030 % 0031 % Outputs 0032 % 0033 % stepsize : norm of the vector retracted to reach newx from x. 0034 % newx : next iterate using the constant stepsize, such that 0035 % the retraction at x of the vector alpha*d reaches newx. 0036 % newkey : key associated to newx in storedb 0037 % lsstats : statistics about the line-search procedure 0038 % (costevals, stepsize, alpha). 0039 % 0040 % See also: steepestdescent conjugategradients linesearch 0041 0042 % This file is part of Manopt: www.manopt.org. 0043 % Original author: Victor Liao, June 13, 2022. 0044 % Contributors: 0045 % Change log: 0046 0047 % Allow omission of storedb. 0048 if ~exist('storedb', 'var') 0049 storedb = StoreDB(); 0050 end 0051 0052 % Obtain user-specified alpha if it exists. 0053 % User should specify their intended alpha by: 0054 % problem.linesearch = @(x,d) alpha; 0055 if canGetLinesearch(problem) 0056 alpha = getLinesearch(problem, x, d); 0057 else 0058 alpha = 1; % default alpha value. 0059 end 0060 0061 % Make the chosen step and compute the cost there. 0062 newx = problem.M.retr(x, d, alpha); 0063 newkey = storedb.getNewKey(); 0064 0065 % As seen outside this function, stepsize is the size of the vector we 0066 % retract to make the step from x to newx. Since the step is alpha*d: 0067 norm_d = problem.M.norm(x, d); 0068 stepsize = alpha * norm_d; 0069 0070 % Return some statistics also, for possible analysis. 0071 % Return some statistics also, for possible analysis. 0072 lsstats.costevals = 0; 0073 lsstats.stepsize = stepsize; 0074 lsstats.alpha = alpha; 0075 end

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