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About 10,000 papers for “constrained optimization”

Constrained Optimization

Ruye Wang · Cambridge University Press eBooks · 2025

Emphasizing how and why machine learning algorithms work, this introductory textbook bridges the gap between the theoretical foundations of machine learning and its practical algorithmic and code-level implementation. Over 85 thorough worked examples, in both Matlab and Python, demonstrate how algorithms are implemented and applied whilst illustrating the end result. Over 75 end-of-chapter problems empower students to develop their own code to implement these algorithms, equipping them with hands-on experience. Matlab coding examples demonstrate how a mathematical idea is converted from equations to code, and provide a jumping off point for students, supported by in-depth coverage of essential mathematics including multivariable calculus, linear algebra, probability and statistics, numerical methods, and optimization. Accompanied online by instructor lecture slides, downloadable Python code and additional appendices, this is an excellent introduction to machine learning for senior undergraduate and graduate students in Engineering and Computer Science.

Cited by 0

Constrained Optimization

Eich-Soellner, Edda · Acervo Digital da Universidade Estadual Paulista (Universidade Estadual Paulista) · 2011

This Demonstration shows the minimization or maximization of a function f (blue) subject to a constraint g=0 (red). The green point shows the optimal solution

Cited by 0

Constrained Optimization

Pietro Garibaldi · 2006

Subject Labour and Demographic Economics Human Resource Management Collection: Oxford Scholarship Online

Cited by 2

Constrained Optimization

Raphael T. Haftka, Zafer Gürdal, Manohar P. Kamat · Solid mechanics and its applications · 1990

Cited by 9

Constrained Optimization

Xin‐She Yang · 2018

In reality, almost all problems have constraints, which can make the search domain quite complicated and irregular. This chapter deals with constrained optimization. In essence, the introduction of slack variables is to reformulate the original optimization problem in a higher-dimensional space such that a boundary imposed by an equality becomes a hyper-surface as viewed from the additional dimension. Whatever the real world problem is, it is usually possible to formulate any constrained optimization problem in a general form. There is no penalty when inequality constraints are true or become tight/exact. Once all the inequality constraints have been converted to equalities, one can use the standard method of Lagrange multipliers. One way to look at Karush-Kuhn-Tucker (KKT) conditions is that it can be considered as a generalized method of Lagrange multipliers. It is worth pointing out that the generalized reduced gradient (GRG) has been implemented in many software packages, including the popular Excel Solver.

Cited by 2

Constrained Optimization

Alfred Stein · Encyclopedia of Environmetrics · 2006

Abstract Constrained optimization aims to find an optimum of a function in the presence of constraints. Constrained optimization generally yields a lower optimum on the optimization function as compared with unconstrained optimization, but it honors the presence of constraints. A simple example concerns maximization of the production of a farm subject to constraints on the amount of fertilizers (say n kg per week) and man hours ( h hours per day). Another example is minimization of leaching towards the environment, subject to constraints on soil parameters, groundwater table and other environmental variables.

Cited by 1

Constrained Optimization

Deeksha Aggarwal, Uttam Kumar · Encyclopedia of earth sciences series/Encyclopedia of earth sciences · 2023

Cited by 0

Constrained optimization

P. Neittaanmäki, Marek Rudnicki, A. Savini · 1996

Abstract In optimization theory, when both objective and constraint functions are linear, the problem is called a linear-programming (LP) problem. The term programming refers to scheduling and not to computer programming. The idea goes back to Dantzig [1963] who put forward mathematical principles of scheduling and planning. There are several ways to write the general form of the LP problem. In the following we adopt the LP problem as a minimization of an objective function with equality constraints and nonnegativity bounds on the design variables. Other LP problems can be easily converted into this form using slack variables.

Cited by 6