minFunc_GradDst.m

function [paraVec, funcVal, funcVec] = ...
  minFunc_GradDst(funcHndl, paraVec, opts, varargin)
% INTRO
%   minimize the objective function via gradient descent
% INPUT
%   funcHndl: function handler (compute the function's value and gradient)
%   paraVec: D x 1 (initial solution)
%   opts: structure (optimization options)
%   varargin: K x 1 (cell array; additional parameters)
% OUTPUT
%   paraVec: D x 1 (optimal solution)
%   funcVal: scalar (function's value of the optimal solution)
%   funcVec: T x 1 (list of function's values through iterations)

% solve the optimization via gradient-based update
lr = opts.lrInit;
gradVecAdjs = zeros(size(paraVec));
funcVec = zeros(opts.epchCnt + 1, 1);
[funcVec(1), ~] = funcHndl(paraVec, [], varargin{:});
for epchIdx = 1 : opts.epchCnt
  % generate the mini-batch partition
  smplIdxLst = GnrtMiniBatc(opts.smplCnt, opts.batcSiz);
  
  % update parameters with mini-batches
  for batcIdx = 1 : numel(smplIdxLst)
    % obtain the function's value and gradient vector of the current solution
    [~, gradVec] = funcHndl(paraVec, smplIdxLst{batcIdx}, varargin{:});

    % compute the adjusted gradient vector
    gradVecAdjs = opts.momentum * gradVecAdjs + gradVec;

    % use gradient to update the solution
    paraVec = paraVec - lr * gradVecAdjs;
  end

  % record related variables
  [funcVal, ~] = funcHndl(paraVec, [], varargin{:});
  funcVec(epchIdx + 1) = funcVal;
  
  % update the learning rate
  if funcVec(epchIdx) > funcVec(epchIdx + 1)
    lr = lr * opts.lrIncrMult;
  else
    lr = lr * opts.lrDecrMult;
  end
end

end