- "Mathematical optimization or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives."
This is the process of finding the best solution to a problem or situation, often by using mathematical models and algorithms.
Linear Programming: This is the most basic form of optimization and involves maximizing or minimizing a linear objective function subject to linear constraints.
Nonlinear Programming: This topic deals with optimizing nonlinear objective functions subject to nonlinear constraints.
Integer Programming: This is a type of optimization where the decision variables are constrained to be integers. This technique is useful in modeling problems with discrete choices.
Convex Optimization: This is a subset of nonlinear programming where the objective function and constraints are convex. This topic is useful in finding an optimal solution that is both feasible and globally optimal.
Dynamic Programming: This is a technique for solving problems where the solution must be found by considering a sequence of decisions over time. This topic is useful in modeling problems with sequential decision-making.
Genetic Algorithms: This is a type of optimization that mimics the process of natural selection to find an optimal solution. This technique is useful when the objective function is complex and cannot be easily modeled mathematically.
Simulated Annealing: This is a technique for finding the global optimum by randomly searching the solution space and gradually reducing the search radius over time. This method is useful in finding the global optimum of complex, nonlinear problems.
Tabu Search: This method involves iteratively selecting a candidate solution and making small modifications to it in order to search for a better solution. This technique is useful in problems with multiple local optima.
Network Optimization: This is a type of optimization where the objective is to minimize the cost of distributing goods or services through a network of nodes and edges. This topic is useful in modeling logistics or transportation problems.
Multi-objective Optimization: This technique deals with the problem of optimizing multiple conflicting objectives simultaneously. This is useful in decision-making when there is more than one objective to be considered.
Linear Programming (LP): LP is a mathematical optimization technique used to optimize an objective function subject to linear constraints. Linear programming is used to make strategic decisions and allocate resources efficiently.
Non-Linear Programming (NLP): Similar to LP, NLP is a mathematical optimization technique. It is used to optimize an objective function subject to non-linear constraints. NLP is used when there are non-linear relationships between the factors that need optimization.
Stochastic Programming (SP): SP is a mathematical optimization Technique. It is used to optimize an objective function in the presence of uncertainty. SP is used when there is a lack of accurate data or there is randomness in the outcomes.
Integer programming (IP): IP is a mathematical optimization technique used when the variable needs to be integer. It is used when strategic, tactical, operational or planning decision or modeling requires an integer variable i.e. where there are discrete values allowed only.
Constraint Programming (CP): CP is a mathematical optimization technique used to find feasible solutions to a problem. CP is used to solve combinatorial optimization problems like scheduling, planning, routing.
Multi-Objective Optimization (MOO): MOO is an optimization technique used to optimize two or more conflicting objectives simultaneously. MOO is used when there are multiple objectives and finding a solution that optimizes all objectives simultaneously would be the best solution.
Metaheuristics: Metaheuristics are a class of optimization algorithms that are used to solve difficult optimization problems that cannot be solved using traditional methods. Examples include simulated annealing, genetic algorithms, and particle swarm optimization.
Convex Optimization: Convex optimization is a type of optimization problem that has a convex function as the objective function, and the constraints are also convex. This kind of optimization is used in many fields like aerospace, civil engineering, automation etc.
- "It is generally divided into two subfields: discrete optimization and continuous optimization."
- "Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics."
- "The development of solution methods has been of interest in mathematics for centuries."
- "An optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function."
- "The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics."
- "More generally, optimization includes finding 'best available' values of some objective function given a defined domain (or input), including a variety of different types of objective functions and different types of domains."
- "Mathematical optimization (alternatively spelled optimisation)..."
- "It is generally divided into two subfields: discrete optimization and continuous optimization."
- "Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics."
- "The development of solution methods has been of interest in mathematics for centuries."
- "An optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function."
- "The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics."
- "More generally, optimization includes finding 'best available' values of some objective function given a defined domain (or input), including a variety of different types of objective functions and different types of domains."
- "Mathematical optimization or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives."
- "It is generally divided into two subfields: discrete optimization and continuous optimization."
- "Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics."
- "The development of solution methods has been of interest in mathematics for centuries."
- "An optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function."
- "More generally, optimization includes finding 'best available' values of some objective function given a defined domain (or input), including a variety of different types of objective functions and different types of domains."