In this thesis, a class of general nonlinear programming problems with inequality and equality constraints is discussed. Firstly, the original problem is transformed into an associated simpler equivalent problem with only inequality constraints. Then, inspired by the ideals of the sequential quadratic programming (SQP) method and the method of system of linear equations (SLE), a new type of SQP algorithm for solving the original problem is proposed. At each iteration, the search direction is generated by the combination of two directions, which are obtained by solving an always feasible quadratic programming (QP) subproblem and a SLE, respectively. Moreover, in order to overcome the Maratos effect, the higher-order correction direction is obtained by solving another SLE. The two SLEs have the same coefficient matrices, and we only need to solve the one of them after a finite number of iterations. By a new line search technique, the proposed algorithm possesses global and superlinear convergence under some suitable assumptions without the strict complementarity. Finally, some comparative numerical results are reported to show that the proposed algorithm is effective and promising

In multi-objective geometric programming problem there are more than one objective
functions. There is no single optimal solution which simultaneously optimizes all the
objective functions. Under these conditions the decision makers always search for the most
‘‘preferred’’ solution, in contrast to the optimal solution. A few mathematical programming
methods namely fuzzy programming, goal programming and weighting methods have
been applied in the recent past to find the compromise solution. In this ‎thesis ‎‎$‎\varepsilon‎‎‎$‎-constraint
method has been applied to find the non-inferior solution. A brief solution procedure of ‎‎$‎\varepsilon‎‎‎$-
constraint method has been presented to find the non-inferior solution of the multi-objective
programming problems. Further, the multi-objective programming problems is solved
by the fuzzy programming technique to find the optimal compromise solution. Finally, two
numerical examples are solved by both the methods and compared with their obtained
solutions.

In this thesis, the linear programming problems is being considered with interval coefficients. We have presented the weak and strong optimality solutions for a linear interval programming. We have investigated the necessary and sufficient condition for a strong optimality condition. Further more we introduce the conditions for obtaining the strong optimality condition for a linear programming problem with interval coefficients .we Finally obtain the necessary and sufficient conditions under which an interval linear programming problem can have the strong form of the interval(A^I و b^I ) and (A^I و b^I و c^I ). We discuss the methods of how to solve such problems. Few numerical examples are given in the end
to illustrate the methodology of the solution.
 

The aim of this thesis is to present an algorithms of fuzzy goal programming (FGP) for solving quadratic bi-level programming (QBLPP) problems whit single objective at the upper level and lower level. A fuzzy goal programming (FGP) algorithm for quadratic bi-level programming (QBLPP) problems is proposed. This algorithm is extended to solve quadratic bi-level programming (QTLPP) problems. In the model formulation of the problem, we construct the quadratic membership function by determining individual best solution of the quadratic objective function subject to the system constraints. The quadratic membership functions are then transformed into equivalent linear membership function by first order Taylor series approximation at the individual best solution point.A posible relaxation of each level decisions are considered by providing preference bounds on the decision variables for avoiding decision deadlock. Then FGP approach is used to achieve highest degree of each of the membership goals by minimizing their deviational variables and there by obtaining the most satisfactory solution for all decision maker. Few numerical examples are provided in order to demonstrate the efficiency of the proposed approach.

 The assignment problem is a specific type of transportation problem in which m tasks should be assigned to m machines. If task i is assigned to machine j, the cost would be equal to Cij. We want to do this assignment in a way that finally has the least price.
In this thesis, the assignment model would be expended in order to offer a dietary plan which suits the determined targets. At first, some mathematical models for dietary plan is investigated and then foods which are served at Chamran University Restaurant is measured in terms of their prices, carbohydrate, fat, calorie and protein and based on assignment model, to offer a weekly dietary plan for the students who are in a good health condition with the aim of minimizing the price or the amount of fat or price or maximizing the amount calories and protein so that the minimum nutritional requirement of students is met.

 . Integer programming is one of the NP hard problem that so far; various methods have been proposed for it       
.Multiple objective optimization problems are very important as modeling too 
In this thesis we introduce an algorithm for computation all of the Nondominated extreme points in the out com set of multiple objective integer problem.
.The main procedur algorithms is decompose the weight space and find Nondominated extrem point simultaneous
.Adjacency for Nondominated extrem points is based on existence the common faces between their weight sets
.We will apply this algorithm on the assignment problem

The theory of the fuzzy numbers play an important role in all the different branch of the science. Recently, scientists have developed new means, of the fuzzy numbers, with new concept of the interval-valued fuzzy numbers, which can be applied in diffirent environmental decissions. But we can use them in our decissions if we be able to stecisy and clear the place and importance of the logic to the DMS.Therefore the ranking of interval-valued fuzzy numbers becomes very important in each and every fuzzy environmental decissions. Ye and Chen presented the accuracy function for intuitionistic fuzzy sets, they also ranked them. Chiang and Shieh used the signed distance for crisping and ranking whit interval-valued fuzzy numbers and fuzzy sets. On considering suggestions, we have shown that we can rank them in better way by our approach. So we can present a better advantage of them in our daily life.

In this thesis, we discuss about the use of multi objective problems in the financial markets. In finance there has always been the problem of how to combine investments to form a portfolio. Progress on this problem, called portfolio selection, did not reach a historical juncture until the 1950s. Markowitz developed his mean-vaiance model, introduced an algorithm for solving for “efficient frontier”, and advised on the selection of one`s optimal portfolio from the efficient frontier. Efficient portfolio is one that has minimum variance (risk) with defined return or maximum return with defined variance (risk).
In this thesis, at first we proceed Markowitz mean-variance model and for more practical use of this approach, the ideas of using higher moments in portfolio optimization problem have been discussed recent years. This idea was introduced by konno and et al for the first time in 1990. The third moment (skewness) plays an important role if the distribution of the rate of return of assets is asymmetric around the mean. In particular, an investor would prefer a portfolio with larger third moment if the mean and variance are the same. At last we introduce multiple objectives models in portfolio selection that its difference is there are some investors have other considerations such as to maximize liquidity or to minimize the amount of short selling and so forth that these result to multiobjective stochastic programming problem that for solving must be transformed to equivalent deterministic problem. Here we solve the optimal portfolio selection problem with these ideas. We use Matlab and NIMBUS softwares for numerical examples. The data are from Tehran Stock Exchange.
 

Non linear programming is one of the branches in the
optimization problems. Particularly when the variables are
integers, classical methods cannot obtain the solution of the
problem. Due to importance of such problems.
In this thesis we discuse the integer non linear programming with
boundary variables; and introduce an approximate method namely
dynamic convexized method.The advantage of this method is
reduce the time to set exact soulation for the problems.