Study of mathematical algorithms for optimization problems
"Optimization" and "Optimum" redirect here. For other uses, see Optimization (disambiguation) and Optimum (disambiguation).
"Mathematical programming" redirects here. For the peer-reviewed journal, see Mathematical Programming.
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Graph of a surface given by z = f(x, y) = −(x² + y²) + 4. The global maximum at (x, y, z) = (0, 0, 4) is indicated by a blue dot.Nelder-Mead minimum search of Simionescu's function. Simplex vertices are ordered by their values, with 1 having the lowest ( best) value.
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives.[1][2] It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering[3] to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.[4]
In the more general approach, 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.
^"The Nature of Mathematical Programming Archived 2014-03-05 at the Wayback Machine," Mathematical Programming Glossary, INFORMS Computing Society.
^"Mathematical Programming: An Overview" (PDF). Retrieved 26 April 2024.
^Martins, Joaquim R. R. A.; Ning, Andrew (2021-10-01). Engineering Design Optimization. Cambridge University Press. ISBN 978-1108833417.
^Du, D. Z.; Pardalos, P. M.; Wu, W. (2008). "History of Optimization". In Floudas, C.; Pardalos, P. (eds.). Encyclopedia of Optimization. Boston: Springer. pp. 1538–1542.
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generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from...
convex optimization problems admit polynomial-time algorithms, whereas mathematicaloptimization is in general NP-hard. A convex optimization problem...
Combinatorial optimization is a subfield of mathematicaloptimization that consists of finding an optimal object from a finite set of objects, where the...
researchers active in optimization. The MOS encourages the research, development, and use of optimization—including mathematical theory, software implementation...
(often referred to as simply, “Gurobi”) is a solver, since it uses mathematicaloptimization to calculate the answer to a problem. Gurobi is included in the...
Bilevel optimization is a special kind of optimization where one problem is embedded (nested) within another. The outer optimization task is commonly referred...
Continuous optimization is a branch of optimization in applied mathematics. As opposed to discrete optimization, the variables used in the objective function...
hyperparameter optimization methods. Bayesian optimization is a global optimization method for noisy black-box functions. Applied to hyperparameter optimization, Bayesian...
Robust optimization is a field of mathematicaloptimization theory that deals with optimization problems in which a certain measure of robustness is sought...
transformation between input and output values, described by a mathematical function, optimization deals with generating and selecting the best solution from...
must be estimated for each technology. In mathematics, mathematicaloptimization (or optimization or mathematical programming) refers to the selection of...
Topology optimization is a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions...
In mathematicaloptimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function...
Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization, some or all of the...
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling...
when the function is at most linear. Linear algebra Mathematicaloptimization Convex optimization Linear programming Quadratic programming Scientific...
Topological optimization techniques can then help work around the limitations of pure shape optimization. Mathematically, shape optimization can be posed...
has several patents awarded. He has worked machine learning and mathematicaloptimization, and more recently on control theory and reinforcement learning...
process of solving certain mathematicaloptimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a...
In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints are not linear equalities or...
developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics...
Dynamic programming is both a mathematicaloptimization method and an algorithmic paradigm. The method was developed by Richard Bellman in the 1950s and...
computational complexity and optimization the no free lunch theorem is a result that states that for certain types of mathematical problems, the computational...
Process optimization is the discipline of adjusting a process so as to optimize (make the best or most effective use of) some specified set of parameters...
An integer programming problem is a mathematicaloptimization or feasibility program in which some or all of the variables are restricted to be integers...
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