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In a narrow sense, foundations of mathematics is the logical and mathematical framework that allows developing mathematics without generating self-contradictory theories, and, in particular, to have reliable concepts of theorems, proofs, algorithms, etc. This includes also the philosophical study of the relation of this framework with the reality.
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue ...
Constrained optimization. In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to ...
Tabu search is a metaheuristic algorithm that can be used for solving combinatorial optimization problems (problems where an optimal ordering and selection of options is desired). Current applications of TS span the areas of resource planning, telecommunications, VLSI design, financial analysis, scheduling, space planning, energy distribution ...
An iterative, non-linear process, design thinking includes activities such as context analysis, user testing, problem finding and framing, ideation and solution generating, creative thinking, sketching and drawing, prototyping, and evaluating . Core features of design thinking include the abilities to: deal with different types of design ...
Troubleshooting. Troubleshooting is a form of problem solving, often applied to repair failed products or processes on a machine or a system. It is a logical, systematic search for the source of a problem in order to solve it, and make the product or process operational again. Troubleshooting is needed to identify the symptoms.
Solver. A solver is a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculates their solution. In a solver, the emphasis is on creating a program or library that can easily ...
Lagrange multiplier. In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables ). [1]