Neutrosophic augmented Lagrange multipliers method Nonlinear Programming Problems Constrained by Inequalities

Operations research uses scientific methods that take the language of mathematics as a basis and uses the computer, without which it would not be possible to achieve numerical solutions to the problems raised. It is concerned with applying scientific methods to complex issues in the management and direction of large systems in various fields and private and governmental businesses in peace and war in politics, management, economics, planning and implementation and in all aspects of life. In issues that require sound solutions, when solutions are numerous and options are multiple, we need a decision based on sound scientific foundations that take into account all the circumstances and changes that the decision maker may face during the course of work, and help him make a decision that leaves nothing to chance or luck. For this reason, operations research has provided many methods that help us transform life issues into mathematical models whose optimal solution is the appropriate decision. The nonlinear programming method is one of the most important methods presented by operations research because most problems, when modeled, result in a nonlinear model, which prompted many students and researchers to search for appropriate scientific methods to solve these models. One of the most important and most widely used of these methods is the Lagrange multipliers method.