example a function or the shape of a body. Such a problem is an infinite-dimensional optimization problem, because, a continuous quantity cannot be determined...

optimal control problem modelling advertising Infinite-dimensional optimization Semi-infinite programming — infinite number of variables and finite number of...

such as those shown above are frequently associated with infinite-dimensional optimization problems with constraints. For example, the Stokes equations...

Random optimization (RO) is a family of numerical optimization methods that do not require the gradient of the optimization problem and RO can hence be...

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

solution. Shape optimization is an infinite-dimensional optimization problem. Furthermore, the space of allowable shapes over which the optimization is performed...

Robust optimization is a field of mathematical optimization theory that deals with optimization problems in which a certain measure of robustness is sought...

problem being optimized, which means DE does not require the optimization problem to be differentiable, as is required by classic optimization methods such...

by using another overlaying optimizer, a concept known as meta-optimization, or even fine-tuned during the optimization, e.g., by means of fuzzy logic...

Biogeography-based optimization (BBO) is an evolutionary algorithm (EA) that optimizes a function by stochastically and iteratively improving candidate...

of optimization methods that sample from a hypersphere surrounding the current position. Random optimization is a related family of optimization methods...

trajectory optimization were in the aerospace industry, computing rocket and missile launch trajectories. More recently, trajectory optimization has also...

possible. Local search is a sub-field of: Metaheuristics Stochastic optimization Optimization Fields within local search include: Hill climbing Simulated annealing...

problems containing variables with infinite domain. These are typically solved as optimization problems in which the optimized function is the number of violated...

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

search (RS) is a family of numerical optimization methods that do not require the gradient of the optimization problem, and RS can hence be used on functions...

In the field of mathematical optimization, stochastic programming is a framework for modeling optimization problems that involve uncertainty. A stochastic...

method (see the Kantorovich theorem). Kantorovich considered infinite-dimensional optimization problems, such as the Kantorovich-Monge problem in transport...

In optimization theory, semi-infinite programming (SIP) is an optimization problem with a finite number of variables and an infinite number of constraints...

In mathematical optimization, fractional programming is a generalization of linear-fractional programming. The objective function in a fractional program...

from a randomly selected subset of the data). Especially in high-dimensional optimization problems this reduces the very high computational burden, achieving...

{\displaystyle K} , and allows us to transform a complicated (possibly infinite dimensional) optimization problem into a simple linear system that can be solved numerically...

for two-dimensional Euclidean geometry). Euclid sometimes distinguished explicitly between "finite lines" (e.g., Postulate 2) and "infinite lines" (book...

Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. For large numbers of local optima, SA...

expansions on the training data, thus reducing an infinite dimensional optimization problem to a finite dimensional one. He co-developed kernel embeddings of...

Variational bicomplex Fermat's principle Principle of least action Infinite-dimensional optimization Finite element method Functional analysis Ekeland's variational...

strategy for numerical optimization. Evolution strategies (ES) are stochastic, derivative-free methods for numerical optimization of non-linear or non-convex...

\end{aligned}}} This space is the infinite-dimensional generalization of the ℓ 2 n {\displaystyle \ell _{2}^{n}} space of finite-dimensional vectors. It is usually...

space is finite-dimensional if its dimension is a natural number. Otherwise, it is infinite-dimensional, and its dimension is an infinite cardinal. Finite-dimensional...

programming equation (DPE) associated with discrete-time optimization problems. In continuous-time optimization problems, the analogous equation is a partial differential...