Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003) 3-51] introduced primal-dual path-following algorithms for solving second-order cone programming problems. In this paper, we generalize their work by using the machinery of Euclidean Jordan alg...

A new method for the efficient solution of free material optimization problems is introduced. The method extends the sequential convex programming (SCP) concept to a class of optimization problems with matrix variables. The basic idea of the new method is to approximate the original optimization problem by a sequence of sub-problems, in which nonlinear functions (defined in matrix variables) ar...

This paper is concerned with the study of duality conditions to convex-concave generalized multiobjective fuzzy nonlinear fractional disjunctive programming problems for which the decision set is the union of a family of convex sets. The Lagrangian function for such problems is defined and the Kuhn-Tucker Saddle and Stationary points are characterized. In addition, some important theorems relat...

An amazing variety of activities and situations can be adequately modeled as linear optimization problems, also known as linear programs (LPs), or convex nonlinear optimization problems. Adequately means that the degree of approximation to reality that such a representation involves is acceptable. However, as the world that we inhabit is neither linear nor convex, the most common obstacle to th...

This paper examines global optimization of an integral objective function subject to nonlinear ordinary differential equations. Theory is developed for deriving a convex relaxation for an integral by utilizing the composition result defined by McCormick (Mathematical Programming 10, 147–175, 1976) in conjunction with a technique for constructing convex and concave relaxations for the solution o...

We propose an SQP-type algorithm for solving nonlinear second-order cone programming (NSOCP) problems. At every iteration, the algorithm solves a convex SOCP subproblem in which the constraints involve linear approximations of the constraint functions in the original problem and the objective function is a convex quadratic function. Those subproblems can be transformed into linear SOCP problems...

The paper examines the applicability of mathematical programming methods to the simultaneous optimization of the structure and the operational parameters of a combined-cycle-based cogeneration plant. The optimization problem is formulated as a non-convex mixed-integer nonlinear problem (MINLP) and solved by the MINLP solver LaGO. The algorithm generates a convex relaxation of the MINLP and appl...

Fuzzy linear regression is an interesting tool for handling uncertain data samples as an alternative to a probabilistic approach. This paper sets forth uses a linear regression model for fuzzy variables; the model is optimized through convex methods. A fuzzy linear programming model has been designed to solve the problem with nonlinear fuzzy data by combining the fuzzy arithmetic theory with co...

in this paper, we conduct a comparative study between the homotopy perturbation method (hpm) and adomian’s decomposition method (adm) for analytic treatment of nonlinear volterra integral equations, and we show that the hpm with a specific convex homotopy is equivalent to the adm for these type of equations.