In the real-world optimization problems, coefficients of the objective function are not known precisely and can be interpreted as fuzzy numbers. In this paper we define the concepts of optimality for linear programming problems with fuzzy parameters (FLP). Then by using the concept of comparison of fuzzy numbers we transform FLP problem into a multiobjective linear programming (MOLP) problem. T...

In this paper we study the behavior of Convex Quadratic Optimization problems when variation occurs simultaneously in the right-hand side vector of the constraints and in the coefficient vector of the linear term in the objective function. It is proven that the optimal value function is piecewise-quadratic. The concepts of transition point and invariancy interval are generalized to the case of ...

Quasi-Newton methods for numerical optimization exploit quadratic Taylor polynomial models of the objective function. Trust regions are widely used to ensure the global convergence of these methods. Analogously, response surface methods for stochastic optimization exploit linear and quadratic regression models of the objective function. Ridge analysis is widely used to safeguard the optimizatio...

In this paper we present optimization problems with biconvex objective function and linear constraints such that the set of global minima of the optimization problems is the same as the set of Nash eqilibria of a n-player general-sum normal form game. We further show that the objective function is an invex function and consider a projected gradient descent algorithm. We prove that the projected...

State of the art classification algorithms are designed to minimize the misclassification error of the system, which is a linear function of the per-class false negatives and false positives. Nonetheless non-linear performance measures are widely used for the evaluation of learning algorithms. For example, F -measure is a commonly used non-linear performance measure in classification problems. ...

The fuzzy optimization problem is one of the prominent topics in the broad area of artificial intelligence. It is applicable in the field of non-linear fuzzy programming. Its application as well as practical realization can been seen in all the real world problems. In this paper a large scale non-linear fuzzy programming problem was solved by hybrid optimization techniques like Line Search (LS)...

We present an algorithm to construct a bounding polyhedron for an affine Iterated Function System (IFS). Our algorithm expresses the IFS-bounding problem as a set of linear constraints on a linear objective function, which can then be solved via standard techniques for linear convex optimization. As such, our algorithm is guaranteed to find the optimum recursively instantiable bounding volume, ...

In the real world, risk and uncertainty are two natural properties in the implementation of Mega projects. Most projects fail to achieve the pre-determined objectives due to uncertainty. A linear integer programming optimization model was used in this work to solve a problem in order to choose the most appropriate risk responses for the project risks. A mathematical model, in which work structu...