• Machine: 193.144.12.89
• user: userX where X{0...10}
• password userX is userX where X{0...10}

     ssh  ssh userX@193.144.12.89
     scp
     scp  route_to_a_file(user machine)  userX@193.144.12.89:route(server machine)
     scp
     scp -r route_to_a_directory(user machine) userX@193.144.12.89:route(server machine)
        

• Linear Programing: The Happiness Problem
• Model
• Using CPLEX solver (terminal)
• Using CPLEX solver (API JAVA)
• Game-Theory and Linear Programming: Two-Person Zero-Sum Games
• Paper-Rock-Scissors Game
• The Ultra Conservative Investor
• Using AMPL + NEOS

              Maximize;       //This is the optimitzation sense.
              obj: 2*P + O;    //This is the objective function.
              Subject to:     //This are the constraints.
              To survive: O >= 56;
              To sanity: P + O >= 70;
              To pass the course: S >= 60;
              For compensation: 2*S + O -3*P >= 150;
              Total Amount of (H) in a week: S + P + O = 168;
              It can be possible not to have fun: P >=0;
              end;

                 $  ./cplex
                 CPLEX>  help
          

               $  ./cplex
               CPLEX>  enter
               CPLEX>  Enter name of the problem: happiness.lp
               CPLEX>  Enter new problem ['end' on a separate line terminates]:
               CPLEX>  //here copy and paste the previous model 
               CPLEX>  optimize
               CPLEX>  display solution objective
               CPLEX>  display solution variables -
          

          import ilog.concert.*;
          import ilog.cplex.*;
          public class Happiness {
          public static void main(String[] args){
          try {
          IloCplex cplex = new IloCplex();
          IloObjective obj = cplex.addMaximize();
          IloRange c1 = cplex.addRange(-infinity, 70.0, "c1");
          IloNumVar P = cplex.numVar(cplex.column(obj,  1.0).and(
          cplex.column(c1,  -1.0).and(cplex.column(c2,   1.0).and(
          cplex.column(c3,   1.0)))),0, infinity, "P");
          cplex.solve();
          System.out.println("f.o: "+cplex.getObjValue());
          System.out.println("P: "+cplex.getValue(P));
          } catch (IloException e) {System.err.println("Concert exception caught: " + e);}}}
      

              Maximize;          //This is the optimitzation sense.
              obj:v              //This is the objective function
              Subject to         //This are the constraints.
                    c1: y - z >= v    (Rock)
                    c2: z - x >= v    (Paper)
                    c3: x - y >= v    (Scissors)
                    c4: x + y + z = 1
              Bounds
                     x >= 0
                     y >= 0
                     z >= 0
              end
              
          

              
                  set ROWS;
                  set COLS;
                  param  {ROWS,COLS} default 0;
                  var x{COLS} >= 0;
                  var v;
                  maximize  zot: v;
                  subject to  ineqs {i in ROWS}:
                    sum {j in COLS} -A[i,j] * x[j] + v < = 0;
                  subject to  equal:
                    sum {j in COLS} x[j] = 1;
              
          

              
                  data;
                  set ROWS := Paper Scissors Rock;
                  set COLS := Paper Scissors Rock;
                  param A:    Paper  Scissors  Rock:=
                    Paper       0        1       -2
                    Scissors   -3        0        4
                    Rock        5       -6        0
                  ;
              
          

              
                  solve;
                  printf {j in COLS}: "%3s %10.7f \n", j, 100*x[j];
                  printf {i in ROWS}: "%3s %10.7f \n", i, 100*ineqs[i];
                  printf "Value = %10.7f \n", 100*v;
              
          

• Lets consider now the historical return on investment data: ROI.
• We can view this as a payoff matrix in a game between Fate and the investor.
• The columns represents pure strategies for our conservative investor.
• The rows represents how history might repeat itself.
• So in 2015, Fate won't just repeat a previous year but, rather will present some mix of these previous years.
• The inverstor won't put all of his money into one asset. Instead he will put a certain fraction into each one.'

• Linear Programming Course of Robert J. Vanderbei
• Introducción a la Teoría de Juegos
• Two-Person Zero-Sum Game
• Ejemplo: El portafoli de Inversión
• Brief Comments on Game Theory
• Linear Programming and Game Theory