This paper incorporates fuzzy random variables with a portfolio selection problem based on the single index model. The rate of return on each investment can be represented with a fuzzy random variable. A novel decision-making model based both on possibilistic programming and on stochastic programming. It is shown that the formulated problem is transformed into the deterministic equivalent nonli...

The modern era of interior-point methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadratic programming, semide nite programming, and nonconvex and nonlinear problems, have reached varyin...

Discrete and continuous nonconvex programming problems arise in a host of practical applications in the context of production planning and control, location-allocation, distribution, economics and game theory, quantum chemistry, and process and engineering design situations. Several recent advances have been made in the development of branch-and-cut type algorithms for mixed-integer linear and ...

This paper addresses the globally optimal solution of the network-constrained unit commitment (NCUC) problem incorporating a nonlinear alternating current (AC) model of the transmission network. We formulate the NCUC as a mixed-integer quadratically constrained quadratic programming (MIQCQP) problem. A global optimization algorithm is developed based on a multi-tree approach that iterates betwe...

This paper presents a sequential optimization technique for the design of optimal trajectories while minimizing a cost index subject to system dynamics, path and actuation constraints. A novel coordinate transformation is introduced to cast the non-convex trajectory generation problem as a convex optimization problem. A sequential linear programming approach is discussed to solve the resulting ...

In this paper we present an improved neural network to solve strictly convex quadratic programming(QP) problem. The proposed model is derived based on a piecewise equation correspond to optimality condition of convex (QP) problem and has a lower structure complexity respect to the other existing neural network model for solving such problems. In theoretical aspect, stability and global converge...

Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increasing functions of the parameter. This family of t-norms covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. In this paper, we study a nonlinear optimization problem in which the constraints are defined as fuzzy relational equations (FRE) with the Dombi...

This paper considers the fixed point problem for a nonexpansive mapping on a real Hilbert space and proposes novel line search fixed point algorithms to accelerate the search. The termination conditions for the line search are based on the well-known Wolfe conditions that are used to ensure the convergence and stability of unconstrained optimization algorithms. The directions to search for fixe...

We present a polynomial-time interior-point algorithm for a class of nonlinear saddle-point problems that involve semidefiniteness constraints on matrix variables. These problems originate from robust optimization formulations of convex quadratic programming problems with uncertain input parameters. As an application of our approach, we discuss a robust formulation of the Markowitz portfolio se...