Topic
Nonlinear programming
About: Nonlinear programming is a research topic. Over the lifetime, 19486 publications have been published within this topic receiving 656602 citations. The topic is also known as: non-linear programming & NLP.
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TL;DR: Techniques which circumvent difficulties if the quadratic programming subproblems become infeasible, or if the associated sequence of search directions is unbounded are considered.
Abstract: The sequential quadratic programming method developed by Wilson, Han and Powell may fail if the quadratic programming subproblems become infeasible, or if the associated sequence of search directions is unbounded. This paper considers techniques which circumvent these difficulties by modifying the structure of the constraint region in the quadratic programming subproblems. Furthermore, questions concerning the occurrence of an unbounded sequence of multipliers and problem feasibility are also addressed.
137 citations
TL;DR: In this paper, a mixed integer non-linear programming (MINLP) approach for determining optimal location and number of distributed generators in hybrid electricity market is presented, which is based on real power nodal price and real power loss sensitivity index as an economic and operational criterion.
Abstract: This study presents mixed integer non-linear programming (MINLP) approach for determining optimal location and number of distributed generators in hybrid electricity market. For optimal location of distributed generation (DG), first the most appropriate zone has been identified based on real power nodal price and real power loss sensitivity index as an economic and operational criterion. After identifying the suitable zone, mixed integer non-linear programming approach has been applied to locate optimal place and number of distributed generators in the obtained zone. The non-linear optimisation approach consists of minimisation of total fuel cost of conventional and DG sources as well as minimisation of line losses in the network. The pattern of nodal real and reactive power prices, line loss reduction and fuel cost saving has been obtained. The results have also been obtained for pool electricity market model for comparison. The impact of demand variation on the results has also been obtained for both the market models. The proposed MINLP-based optimisation approach has been applied for IEEE 24 bus reliability test system.
137 citations
TL;DR: In this paper, the collocation method meshed with non-linear programming techniques provides an efficient strategy for the numerical solution of optimal control problems, and good accuracy can be obtained for the state and the control trajectories as well as for the value of the objective function.
Abstract: The collocation method meshed with non-linear programming techniques provides an efficient strategy for the numerical solution of optimal control problems. Good accuracy can be obtained for the state and the control trajectories as well as for the value of the objective function. In addition, the control strategy can be quite flexible in form. However, it is necessary to select the appropriate number of collocation points and number of parameters in the approximating functions with care.
137 citations
TL;DR: An algorithm is developed for solving the convex programming problem by constructing a cutting plane through the center of a polyhedral approximation to the optimum, which generates a sequence of primal feasible points whose limit points satisfy the Kuhn—Tucker conditions of the problem.
Abstract: An algorithm is developed for solving the convex programming problem which iteratively proceeds to the optimum by constructing a cutting plane through the center of a polyhedral approximation to the optimum. This generates a sequence of primal feasible points whose limit points satisfy the Kuhn—Tucker conditions of the problem. Additionally, we present a simple, effective rule for dropping prior cuts, an easily calculated bound on the objective function, and a rate of convergence.
137 citations
28 Jan 2001
TL;DR: An optimal load shedding strategy for power systems with multiple distributed generation is presented and the dynamic and static models of each type following a major disturbance are developed.
Abstract: An optimal load shedding strategy for power systems with multiple distributed generation is presented. According to distributed generation's role in emergency state, they are classified as the central generation type, nondispatchable type and storage type. The dynamic and static models of each type following a major disturbance are developed. Based on the analysis of a major disturbance in a grid system, interconnection or distributed generation system, the load shedding is formulated as an optimization problem subject to system, operation and security constraints. To handle the differential equations that represent the dynamics of different types of generators, a discretization technique is used to transfer differential equations into algebraic equations. The final nonlinear optimization problem is then solved by mathematical programming. The method is first tested on a small system. Then a 30-bus distribution system with multiple distributed generation is adopted to test the proposed method for a more practical application.
137 citations