In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives...

Strong duality is a condition in mathematical optimization in which the primal optimal objective and the dual optimal objective are equal. By definition...

belong to a larger class of duality theorems in optimization. The strong duality theorem is one of the cases in which the duality gap (the gap between the...

In applied mathematics, weak duality is a concept in optimization which states that the duality gap is always greater than or equal to 0. This means that...

Dual abelian variety Dual basis Dual (category theory) Dual code Duality (electrical engineering) Duality (optimization) Dualizing module Dualizing sheaf...

formalization of mathematical duality Duality (optimization) Duality (order theory), a concept regarding binary relations Duality (projective geometry), general...

generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from...

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently...

principle (Boolean algebra) Duality principle for sets Duality principle (optimization theory) Lagrange duality Duality principle in functional analysis...

In mathematical optimization, Wolfe duality, named after Philip Wolfe, is type of dual problem in which the objective function and constraints are all...

Conic optimization is a subfield of convex optimization that studies problems consisting of minimizing a convex function over the intersection of an affine...

programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject...

topology Dual wavelet Duality (optimization) Duality (order theory) Duality of stereotype spaces Duality (projective geometry) Duality theory for distributive...

In optimization problems in applied mathematics, the duality gap is the difference between the primal and dual solutions. If d ∗ {\displaystyle d^{*}}...

employed for MRF optimization. Dual decomposition is applied to markov logic programs as an inference technique. Discrete MRF Optimization (inference) is...

conjugate is widely used for constructing the dual problem in optimization theory, thus generalizing Lagrangian duality. Let X {\displaystyle X} be a real topological...

Riemannian manifold Duality (optimization) Weak duality — dual solution gives a bound on the primal solution Strong duality — primal and dual solutions are...

Bayesian optimization is a sequential design strategy for global optimization of black-box functions, that does not assume any functional forms. It is...

Convex preferences Expenditure minimization problem Slutsky equation Duality (optimization) Hicks–Marshall laws of derived demand Jonathan Levin; Paul Milgrom...

Slater condition) is a sufficient condition for strong duality to hold for a convex optimization problem, named after Morton L. Slater. Informally, Slater's...

polynomial, a concept called roof duality can be used to obtain a lower bound for its minimum value. Roof duality may also provide a partial assignment...

Multi-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute...

of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate...

but curved, and the degree of curvature is called the convexity. Duality (optimization) Epigraph (mathematics) - for a function f : Rn→R,[check spelling]...

profile-guided optimization (PGO, sometimes pronounced as pogo), also known as profile-directed feedback (PDF) or feedback-directed optimization (FDO), is...

closes the duality gap. Necessity: any solution pair x ∗ , ( μ ∗ , λ ∗ ) {\displaystyle x^{*},(\mu ^{*},\lambda ^{*})} must close the duality gap, thus...

the performance of the system. Topology optimization is different from shape optimization and sizing optimization in the sense that the design can attain...

A sum-of-squares optimization program is an optimization problem with a linear cost function and a particular type of constraint on the decision variables...

traditional definition of Fenchel duality. Radu Ioan Boţ; Gert Wanka; Sorin-Mihai Grad (2009). Duality in Vector Optimization. Springer. ISBN 978-3-642-02885-4...

France. In mathematical optimization, Claude Lemaréchal is known for his work in numerical methods for nonlinear optimization, especially for problems...