Non-smoothness and non-convexity in optimization problems often arise because a combinatorial structure is imposed on smooth or convex data. The combinatorial aspect can be explicit, e.g. through the use of ”max”, ”min”, or ”if” statements in a model, or implicit as in the case of bilevel optimization where the combinatorial structure arises from the possible choices of active constraints in th...

The optimal reactive power dispatch (ORPD) is a very important problem aspect of power system planning and is a highly nonlinear, non-convex optimization problem because consist of both continuous and discrete control variables. Since the power system has inherent uncertainty, hereby, this paper presents both of the deterministic and stochastic models for ORPD problem in multi objective and sin...

Recently, Particle Swarm Optimization (PSO) has been applied to various application fields. In this paper, a new optimization method “α Constrained Particle Swarm Optimizer (αPSO)”, which is the combination of the α constrained method and PSO, is proposed. The αPSO is applied to several test problems such as nonlinear programming problems and problems with non-convex constraints. It is compared...

The Optimizer proposed in this paper addresses the problem of running a gas turbine optimally to maximize the operational profit of a power utility subject to fluctuating energy prices and changing operating conditions. The proposed optimization scheme determines the optimal load profile of a gas turbine that maximizes the operational profit generated from sale of electricity subject to fuel co...

in this article the general non-symmetric parametric form of the incremental secant stiffness matrix for nonlinear analysis of solids have been investigated to present a semi analytical sensitivity analysis approach for geometric nonlinear shape optimization. to approach this aim the analytical formulas of secant stiffness matrix are presented. the models were validated and used to perform inve...

Power flow optimization is generally nonlinear and non-convex, and a second-order cone relaxation has been proposed recently for convexification. We prove several sufficient conditions under which the relaxation is exact. One of these conditions seems particularly realistic and suggests guidelines on integrating distributed generations.

This paper addresses the problem of generating cuts for mixed integer nonlinear programs where the objective is linear and the relations between the decision variables are described by convex functions defining a convex feasible region. We propose a new method for strengthening the continuous relaxations of such problems using cutting planes. Our method can be seen as a practical implementation...