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JOptimizer is a java library for solving general convex optimization problems, like for example LP, QP, QCQP, SOCP, SDP, GP and many more.
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/*
 * Copyright 2011-2017 joptimizer.com
 *
 * This work is licensed under the Creative Commons Attribution-NoDerivatives 4.0 
 * International License. To view a copy of this license, visit 
 *
 *        http://creativecommons.org/licenses/by-nd/4.0/ 
 *
 * or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.
 */
package com.joptimizer.optimizers;

import org.apache.commons.lang3.ArrayUtils;
import org.apache.commons.logging.Log;
import org.apache.commons.logging.LogFactory;

import com.joptimizer.exception.IterationsLimitException;
import com.joptimizer.exception.JOptimizerException;
import com.joptimizer.functions.StrictlyConvexMultivariateRealFunction;
import com.joptimizer.solvers.BasicKKTSolver;
import com.joptimizer.solvers.KKTSolver;
import com.joptimizer.util.ColtUtils;

import cern.colt.matrix.tdouble.DoubleMatrix1D;
import cern.colt.matrix.tdouble.DoubleMatrix2D;

/**
 * @see "S.Boyd and L.Vandenberghe, Convex Optimization, p. 487"
 * @author alberto trivellato ([email protected])
 */
public class NewtonUnconstrained extends OptimizationRequestHandler {

	private static Log log = LogFactory.getLog(NewtonUnconstrained.class.getName());
	
	public NewtonUnconstrained(boolean activateChain){
		if(activateChain){
			this.successor = new NewtonLEConstrainedFSP(true);
		}
	}
	
	public NewtonUnconstrained(){
		this(false);
	}

	@Override
	public void optimize() throws JOptimizerException {
		if(log.isDebugEnabled()){
			log.debug("optimize");
		}
		OptimizationResponse response = new OptimizationResponse();

		// checking responsibility
		if (getA() != null || getFi() != null) {
			// forward to the chain
			forwardOptimizationRequest();
			return;
		}
		if (getF0() instanceof StrictlyConvexMultivariateRealFunction) {
			// OK, it's my duty
		} else {
			throw new JOptimizerException("Unsolvable problem");
		}

		long tStart = System.currentTimeMillis();
		DoubleMatrix1D X0 = getInitialPoint();
		if (X0 == null) {
			X0 = F1.make(getDim());
		}
		if(log.isDebugEnabled()){
			log.debug("X0:  " + ArrayUtils.toString(X0.toArray()));
		}

		DoubleMatrix1D X = X0;
		double previousLambda = Double.NaN;
		int iteration = 0;
		while (true) {
			iteration++;
			double F0X = getF0(X);
			if(log.isDebugEnabled()){
				log.debug("iteration " + iteration);
				log.debug("X=" + ArrayUtils.toString(X.toArray()));
				log.debug("f(X)=" + F0X);
			}
			
			// custom exit condition
			if(checkCustomExitConditions(X)){
				break;
			}
			
			DoubleMatrix1D gradX = getGradF0(X);
			DoubleMatrix2D hessX = getHessF0(X);

			// Newton step and decrement
			DoubleMatrix1D step = calculateNewtonStep(hessX, gradX);
			//DoubleMatrix1D step = calculateNewtonStepCM(hessX, gradX);
			if(log.isDebugEnabled()){
				log.debug("step: " + ArrayUtils.toString(step.toArray()));
			}

			//Newton decrement
			double lambda = Math.sqrt(-ALG.mult(gradX, step));
			if(log.isDebugEnabled()){
				log.debug("lambda: " + lambda);
			}
			if (lambda / 2. <= getTolerance()) {
				break;
			}
			
			// iteration limit condition
			if (iteration == getMaxIteration()) {
				log.error(IterationsLimitException.MAX_ITERATIONS_EXCEEDED);
				throw new IterationsLimitException(IterationsLimitException.MAX_ITERATIONS_EXCEEDED);
			}
			
			// progress conditions
			if(isCheckProgressConditions()){
				if(log.isDebugEnabled()){
					log.debug("previous: " + previousLambda);
				}
				if (!Double.isNaN(previousLambda) && previousLambda <= lambda) {
					log.error("No progress achieved, exit iterations loop without desired accuracy");
					throw new JOptimizerException("No progress achieved, exit iterations loop without desired accuracy");
				} 
			}
			previousLambda = lambda;
			
			// backtracking line search
			double s = 1d;
			DoubleMatrix1D X1 = null;
			int cnt = 0;
			while (cnt < 25) {
              cnt++;
				// @TODO: can we use semplification 9.7.1 (Pre-computation for line searches)?
				//X1 = X.copy().assign(step.copy().assign(Mult.mult(s)), Functions.plus);// x + t*step
				X1 = ColtUtils.sum(X, step, s);
				double condSX = getF0(X1);
				//NB: this will also check !Double.isNaN(getF0(X1))
				double condDX = F0X + getAlpha() * s * ALG.mult(gradX, step);
				if (condSX <= condDX) {
					break;
				}
				s = getBeta() * s;
			}
			if(log.isDebugEnabled()){
				log.debug("s: " + s);
			}

			// update
			X = X1;
		}

		long tStop = System.currentTimeMillis();
		if(log.isDebugEnabled()){
			log.debug("time: " + (tStop - tStart));
		}
		response.setSolution(X.toArray());
		setOptimizationResponse(response);
	}

  //@TODO: can we use semplification 9.7.2 ??
	//NB: the matrix hessX is square
	//Hess.step = -Grad
	private DoubleMatrix1D calculateNewtonStep(DoubleMatrix2D hessX, DoubleMatrix1D gradX) throws JOptimizerException {
		//KKTSolver kktSolver = new BasicKKTSolver();
		KKTSolver kktSolver = new BasicKKTSolver();
		if(isCheckKKTSolutionAccuracy()){
			kktSolver.setCheckKKTSolutionAccuracy(isCheckKKTSolutionAccuracy());
			kktSolver.setToleranceKKT(getToleranceKKT());
		}
		kktSolver.setHMatrix(hessX);
		kktSolver.setGVector(gradX);
		DoubleMatrix1D[] sol = kktSolver.solve();
		DoubleMatrix1D step = sol[0];
		return step;
	}
	
}