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An Overview
Published in Slobodan P. Simonović, Managing Water Resources, 2012
Nonlinear programming is an optimization approach used to solve problems when the objective function and the constraints are not all in the linear form. In general, the solution to a nonlinear problem is a vector of decision variables which optimizes a nonlinear objective function subject to a set of nonlinear constraints. No algorithm exists that will solve every specific problem fitting this description. However, substantial progress has been made for some important special cases by making various assumptions about these functions. Successful applications are available for special classes of nonlinear programming problems such as unconstrained problems, linearly constrained problems, quadratic problems, convex problems, separable problems, non-convex problems and geometric problems.
Devising and Synthesis of Mems and Nems
Published in Sergey Edward Lyshevski, Mems and Nems, 2018
Nonlinear programming is a much more difficult problem compared with the linear programming. As a result, the special cases have been studied. The solution is found if the constraints gi(x) and hj(x) are linear (the linearly constrained optimization problem). If the objective function F(x) is quadratic, the problem is called quadratic programming. One of the greatest challenges in nonlinear programming is the issues associated with the local optima where the requirements imposed on the derivatives of the functions are satisfied. Algorithms that overcome this difficulty are called the global optimization algorithms, and the corresponding techniques are available.
Devising and Synthesis of NEMS and MEMS
Published in Sergey Edward Lyshevski, Nano- and Micro-Electromechanical Systems, 2018
Nonlinear programming is a much more difficult problem compared with linear programming. As a result, special cases have been studied. The solution is found if the constraints gi(x) and hj(x) are linear (the linearly constrained optimization problem). If the objective function F(x) is quadratic, the problem is called quadratic programming. One of the greatest challenges in nonlinear programming is the issues associated with the local optima where the requirements imposed on the derivatives of the functions are satisfied. Algorithms that overcome this difficulty are called the global optimization algorithms, and the corresponding techniques are available.
Event-triggered dual-mode predictive control for constrained nonlinear NCSs subject to disturbances and packet dropouts
Published in International Journal of Control, 2023
The considered MPC problem is a nonlinear programming problem, which can be solved by several common algorithms, such as sequential quadratic programming, interior point approaches and trust region reflective algorithms. There are some standard nonlinear programming solvers to solve problem , e.g. fmincon, ICLOCS toolbox in MATLAB and IPOPT. The time required to solve problem depends on the complexity of problem (e.g. length of prediction horizon and forms of constraints ) and the applied algorithm.
Innovative AI-based multi-objective mixture design optimisation of CPB considering properties of tailings and cement
Published in International Journal of Mining, Reclamation and Environment, 2023
Ehsan Sadrossadat, Hakan Basarir, Ali Karrech, Mohamed Elchalakani
Furthermore, the mixture design problem is commonly a multi-objective multi-constraint optimisation problem with a set of linear and or nonlinear objectives and constraints which may conflict. Objectives and constraints might be nonlinear in this subject. Therefore, algorithms such as linear programming and simplex methods are not applicable for all problems except for those where objectives and constraints are linear. In each run, metaheuristics may find different sub-optimal solutions but with a degree of accuracy. Traditional nonlinear programming (NLP) methods usually find one solution which might be a local optima and cannot search neighbourhood of the local optima to find other local optimum solutions or global optimum. When it comes to a large number of variables they fail to find solution. More importantly, when it comes to multi-objective optimisation, a set of trade-off solutions is anticipated rather than one solution as objectives may conflict. One objective may increase with the increase of variable(s) while the other may decrease. This conflict leads to sacrifice of one objective when it comes to optimisation (maximisation/minimisation). Therefore, a set of trade-off solutions is preferable. These trade off solutions are called Pareto-optimum (Pareto-optimal or Pareto front) solutions rather than optimum. In the present paper, a variant of metaheuristic algorithms, namely non-dominated sorting genetic algorithm (NSGA-II) is used to find the optimal mix designs of CPB meeting the project specific requirements.
MOS Amplifier Design Methodology for Optimum Performance
Published in IETE Journal of Research, 2020
Abir J. Mondal, Paromita Bhattacharjee, Pinaki Chakraborty, Bidyut K. Bhattacharyya
Optimization is a process of providing the best possible solution for a problem with regard to a given situation. It includes maximizing or minimizing an objective function relative to some constraints, which usually extends over a range of available choices. Depending on the nature of objective function and constraints, mathematical optimization problem can be distinguished into many categories. Broadly, it can be categorized into linear programming and NLP optimization problem. With respects to only constraint equations, optimization problem can be unconstrained, linearly constrained or nonlinearly constrained. Linear programming has a strict restriction on both of its objective function and constraint equations to be in linear form. Many methods have been developed to solve linear programming problems. One of the most popular is the simplex method invented in 1947 by Dantzig, an American mathematical scientist, for solving the linear programming problems that arose in U.S. Air Force planning problems [11]. Nonlinear programming is another technique to solve an optimization problem, where an objective function f has to be minimized or maximized subject to some constraint equations gi. It is worthy to mention that either of the objective function or constraint equation can be nonlinear. Therefore, analog circuit problems having linear and nonlinear equations in terms of voltage, current or any design parameter can readily be optimized using NLP.