# Decision making is the most important aspect of any matter one confronts in the physical world. The

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Decision making is the most important aspect of any matter one confronts in the physical world. The success or failure of a project, business, operation, company etc. is directly proportional to the logical reasoning carried out to reach a decision. Bad/ suboptimal decisions can ruin/damage business, project, reputation and careers. Past few decades of research into the decision making paradigm has highlighted that bad decisions are a byproduct of distortions and biases that incapacitate our reasoning. Most of our decision making is heuristic in nature that serves perfectly well in most of the situations. However, when the problem is large enough, one tends to ignore or poorly identify the details that must be taken into account in order…show more content…
The problem of finding an optimal solution under given constraints belongs to the discipline of mathematical optimization that includes methods like linear programming, dynamic programming, integer programming, Pontryagin’s maximum principle and nonlinear programming. Linear programming has been popular since its introduction and has helped solve many real world problems yet it suffers from a grave limitation i.e. the real world is not linear which restricts its use to linear optimization problems or to the ones that can be approximated as linear models. Problems with strong nonlinearities will not give a feasible solution if approximated via linear models. Nonlinear programming addresses these limitations but is far more difficult to implement and needs more computational power to solve problems. In this paper we review the nonlinear programming technique and the way it can help solve a complex optimization problem. The paper is organized as follows. In section 2 we define the optimization problem and its mathematics. In section 3 we discuss the nonlinear programming, its origin, uses and the software programs that can be used to aid problem solving. Section 4 is an example of optimization problem and its solution via nonlinear programming. In section 5, we give the conclusion.
2. Optimization Problem
Mathematically an optimization problem is defined as follows: where is called the objective or cost function to be optimized subject to m inequality constraints