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Topics referred to by the same term
Cost function In economics, the cost curve, expressing production costs in terms of the amount produced. In mathematical optimization, the loss function
Cost_function
Graph used in economics
In economics, a cost curve is a graph of the costs of production as a function of total quantity produced. In a free market economy, productively efficient
Cost_curve
Cost added by producing one additional unit of a product or service
the cost function C {\displaystyle C} is continuous and differentiable, the marginal cost M C {\displaystyle MC} is the first derivative of the cost function
Marginal_cost
Cost function in economics
economics, a cost function represents the minimum cost of producing a quantity of some good. The long-run cost curve is a cost function that models this
Long-run_cost_curve
Mathematical relation assigning a probability event to a cost
optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one
Loss_function
Concept in economics
the same production cost function, the one with the better technology should monopolize the entire market such that the total cost is minimized, thus causing
Natural_monopoly
System that regulates the formation of blocks on a blockchain
provider. This idea is also known as a CPU cost function, client puzzle, computational puzzle, or CPU pricing function. Another common feature is built-in
Proof_of_work
Economic formula of productivity
econometrics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the relationship
Cobb–Douglas production function
Cobb–Douglas_production_function
Procedure for scheduling data packets in a packet switched best-effort network
simultaneously. The cost function would correspond to the number of blocked nearby base station sites. If there are large differences between the "cost" of each
Maximum_throughput_scheduling
Economic price index
developed to approximate the cost of living index. A Konüs index is a type of cost-of-living index that uses an expenditure function such as one used in assessing
Cost-of-living_index
generalized-Ozaki (GO) cost function is a general description of the cost of production proposed by Shinichiro Nakamura. The GO cost function is notable for explicitly
Generalized Ozaki cost function
Generalized_Ozaki_cost_function
Study of optimal transportation and allocation of resources
R 2 {\displaystyle \mathbb {R} ^{2}} . Suppose also that we have a cost function c : R 2 × R 2 → [ 0 , ∞ ) {\displaystyle c:\mathbb {R} ^{2}\times \mathbb
Transportation theory (mathematics)
Transportation_theory_(mathematics)
Production scheduling model
production cost) The single-item EOQ formula finds the minimum point of the following cost function: Total Cost = purchase cost or production cost + ordering
Economic_order_quantity
Inventory theory process
order cost per replenishment c {\displaystyle c} = unit production cost h {\displaystyle h} = annual unit holding cost k {\displaystyle k} = cost per stockout
(Q,r)_model
Lemma
states that if indifference curves of the expenditure or cost function are convex, then the cost-minimizing point of a given good ( i {\displaystyle i}
Shephard's_lemma
Optimization algorithm for artificial neural networks
encoded by the one-hot/dummy variable (e.g., (0,1,0)). C: loss function or "cost function" For classification, this is usually cross-entropy (XC, log loss)
Backpropagation
Linear optimal control technique
minimum cost. The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is
Linear–quadratic_regulator
Algorithm used for pathfinding and graph traversal
on the path, g(n) is the cost of the path from the start node to n, and h(n) is a heuristic function that estimates the cost of the cheapest path from
A*_search_algorithm
Advanced method of process control
dynamic model of the process a cost function J over the receding horizon an optimization algorithm minimizing the cost function J using the control input u
Model_predictive_control
{\displaystyle z} is the inverse distribution function of a standard normal distribution. The total cost is given by the sum of holdings costs and backorders
Base_stock_model
Necessary condition for optimality associated with dynamic programming
minimizing cost, maximizing profits, maximizing utility, etc. The mathematical function that describes this objective is called the objective function. Dynamic
Bellman_equation
Boosting algorithm
considers AdaBoost as a generalized additive model and then applies the cost function of logistic regression, one can derive the LogitBoost algorithm. LogitBoost
LogitBoost
System with self-optimizing transfer function
how to modify the filter transfer function to minimize the cost on the next iteration. The most common cost function is the mean square of the error signal
Adaptive_filter
Optimizing objective functions that have constrained variables
objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy
Constrained_optimization
Distribution estimation technique
Size (ESS). Variance is not the only possible cost function for a simulation, and other cost functions, such as the mean absolute deviation, are used
Importance_sampling
Money spent to produce or procure goods or services
motivation. Average cost Cost accounting Cost curve Cost object Direct cost Fixed cost Incremental cost Indirect cost Life-cycle cost Non-monetary economy
Cost
Combination of losses of goods
e. AFC = TFC/q. The average fixed cost function continuously declines as production increases. Average variable cost (A.V.C) = variable costs divided by
Economic_cost
Study of mathematical algorithms for optimization problems
solutions. The function f is variously called an objective function, criterion function, loss function, cost function (minimization), utility function or fitness
Mathematical_optimization
Distance function defined between probability distributions
Assume also that there is given some cost function c ( x , y ) ≥ 0 {\displaystyle c(x,y)\geq 0} that gives the cost of transporting a unit mass from the
Wasserstein_metric
Statistical algorithm
{\displaystyle {\hat {\mathbf {h} }}(n)} which minimize a cost function. We start by defining the cost function as C ( n ) = E { | e ( n ) | 2 } {\displaystyle
Least_mean_squares_filter
Statistical modeling method
squares cost function as in ridge regression (L2-norm penalty) and lasso (L1-norm penalty). Use of the Mean Squared Error (MSE) as the cost on a dataset
Linear_regression
American economist
microeconomics: if the cost function of a firm is linear, then the total variable cost is proportional to the production volume and the marginal cost is constant
Joel_Dean_(economist)
System used in computer graphics applications
minimum cost function If the minimum cost function occurs at origin, stop the search and set motion vector to (0,0) If the minimum cost function occurs
Block-matching_algorithm
Model in inventory management
{\displaystyle {\frac {1}{2}}hD(1-x)t} Average ordering and holding cost as a function of time: x ( t ) = 1 2 h D ( 1 − x ) t + K t {\displaystyle x(t)={\frac
Economic_production_quantity
Line-breaking algorithm used in the TeX typesetting package
as the algorithm designed by Plass in his PhD thesis. Typically, the cost function for this technique should be modified so that it does not count the
Knuth–Plass line-breaking algorithm
Knuth–Plass_line-breaking_algorithm
Facial recognition system
128-dimensional Euclidean space. The system uses the triplet loss function as its cost function and introduced a new online triplet mining method. The system
FaceNet
Quantum Mechanics in Neural Networks
actual output, the cost function is optimized when C ( w , b ) {\displaystyle C(w,b)} = 0. For a quantum neural network, the cost function is determined by
Quantum_neural_network
Mathematical optimization method
results for non-convex functions. For convergence to critical points: For example, if the cost function is a real analytic function, then it is shown in
Backtracking_line_search
minimal-cost solution (according to a cost function) among multiple possible solutions. A Weighted Constraint Network (WCN), a.k.a. Cost Function Network
Weighted constraint satisfaction problem
Weighted_constraint_satisfaction_problem
Mathematical way of attaining a desired output from a dynamic system
car, speed limits, etc. A proper cost function will be a mathematical expression giving the traveling time as a function of the speed, geometrical considerations
Optimal_control
Total economic cost of production
Marketing Project. Fuss, M. A. (2010) [1987 (print)]. "Production and Cost Functions". In Eatwell, John; Milgate, Murray; Newman, Peter (eds.). The New Palgrave
Total_cost
Combinatorial optimization problem
statement resembles that of the assignment problem, except that the cost function is expressed in terms of quadratic inequalities, hence the name. The
Quadratic_assignment_problem
Tool for analyzing potential welfare costs and benefits of mergers between firms
a function of quantity. Which is necessary for application of Cournot theory. Each firm's residual demand curve intersects above its marginal cost curve
Merger_simulation
Set of constraints conceptualised as a border
marginal cost function is the slope of the total cost function. Thus, given a continuous and differentiable cost function, the marginal cost function is the
Margin_(economics)
Combinatorial optimization problem
the cost function is written down as: ∑ a ∈ A C a , f ( a ) {\displaystyle \sum _{a\in A}C_{a,f(a)}} The problem is "linear" because the cost function to
Assignment_problem
Process of finding a spatial transformation that aligns two point clouds
{S}}}K(x,s)} The cost function can then be shown to be the correlation of the two kernel density estimates: Having established the cost function, the algorithm
Point-set_registration
Linear optimal control technique
}(T)F{\mathbf {x} }(T)} of the cost function becomes negligible and irrelevant to the problem. Also to keep the costs finite the cost function has to be taken to
Linear–quadratic–Gaussian control
Linear–quadratic–Gaussian_control
Property of a computational problem
subset has its own cost function. The minima of each of these cost functions can be found, as can the minima of the global cost function, restricted to the
Optimal_substructure
Collective decision-making procedure
various issues. The number of votes to add is determined by a quadratic cost function, which means that the number of votes a person casts for a given issue
Quadratic_voting
Method in computer modeling
interpolation (OI). An alternative approach is to iteratively solve a cost function that solves an identical problem. These are called "variational methods"
Data_assimilation
Halting output when costs are excessive
the average variable cost curve. Assume that a firm's total cost function is TC = Q3 -5Q2 +60Q +125. Then its variable cost function is Q3 –5Q2 +60Q, and
Shutdown_(economics)
Objective function of evolutionary algorithm
A fitness function is a particular type of objective or cost function that is used to summarize, as a single figure of merit, how close a given candidate
Fitness_function
Technique in numerical linear algebra
lower rank. More precisely, it is a minimization problem, in which the cost function measures the fit between a given matrix (the data) and an approximating
Low-rank_approximation
Combinatorial optimization problem
w.r.t. above cost function. QUBO is very closely related and computationally equivalent to the Ising model, whose Hamiltonian function is defined as
Quadratic unconstrained binary optimization
Quadratic_unconstrained_binary_optimization
local search algorithm. For each feature f i {\displaystyle f_{i}} a cost function c i {\displaystyle c_{i}} is defined. Each feature is also associated
Guided_local_search
Algorithms for matrix decomposition
regularization (akin to Lasso) is added to NMF with the mean squared error cost function, the resulting problem may be called non-negative sparse coding due
Non-negative matrix factorization
Non-negative_matrix_factorization
Class of games in game theory
is a delay function d e : N ⟶ R {\displaystyle d_{e}:\mathbb {N} \longrightarrow \mathbb {R} } (also called latency function or cost function). Given a
Congestion_game
Design concept in economics
marginal cost - the more is produced, the harder it becomes to produce more units (i.e., the cost is a convex function of the demand). An example cost-function
Cost-sharing_mechanism
Mathematical function in economics
revenue equals marginal cost (MC). To derive MC the first derivative of the total cost function is taken. For example, assume cost, C, equals 420 + 60Q +
Inverse_demand_function
Type of set in mathematics
the cost for x goes to 0 as x increases. For instance, the standard cost function has this property. The construction essentially waits until the cost is
K-trivial_set
Problem optimization method
trajectory 𝐱∗ on a continuous time interval t0≤t≤t1 that minimizes a cost function J=b(𝐱(t1),t1)+∫t0t1f(𝐱(t),𝐮(t),t)dt The solution to this problem
Dynamic_programming
Function that maps an observation to an action
this case the set of actions is the parameter space, and a loss function details the cost of the discrepancy between the true value of the parameter and
Decision_rule
Adaptive filter algorithm for digital signal processing
finds the coefficients that minimize a weighted linear least squares cost function relating to the input signals. This approach is in contrast to other
Recursive least squares filter
Recursive_least_squares_filter
Then we hypothesize that the actual muscle forces minimize a given cost function, Φ(𝐅MT), subject to equality and inequality constraints. We have then
Inverse dynamics-based static optimization
Inverse_dynamics-based_static_optimization
Computer vision algorithm
adjacent pixels, with a cost function in the form E(𝒅)=∑pD(p,dp)+∑p,q∈𝒩R(p,dp,q,dq) where D(p,dp) is the pixel-wise dissimilarity cost at pixel p with disparity
Semi-global_matching
so that the steer angle is not directed into an obstacle. Cost function: a cost function was added to better characterize the performance of the algorithm
Vector_Field_Histogram
Set of related ordination techniques used in information visualization
using a procedure called stress majorization. Metric MDS minimizes the cost function called “stress” which is a residual sum of squares: Stress D ( x 1
Multidimensional_scaling
Management accounting term
business units or other cost centres, for example a personnel department, the logistics function, or a canteen. The main function of a cost centre is the tracing
Cost_centre
Maximized objective function of an optimization problem
referred to as "cost-to-go function." In an economic context, where the objective function usually represents utility, the value function is conceptually
Value_function
traveller, increasing the journey time for all travellers. The generalised cost function can be expanded to reflect this congestion delay. g = p + u ( w ) +
Generalised_cost
finite state space. In case of need, one must as well approximate the cost function for one that matches up the Markov chain chosen to approximate the original
Markov chain approximation method
Markov_chain_approximation_method
Ratio in Mathematical Optimization
gap is bounded in several cases. For example, when the cost function is a submodular set function (as in the above example), the correlation gap is at most
Correlation_gap
Mathematical model to assist inventory levels
cumulative distribution function of D {\displaystyle D} . Intuitively, this ratio, referred to as the critical fractile, balances the cost of being understocked
Newsvendor_model
Order-preserving mathematical function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept
Monotonic_function
Process of reducing the number of random variables under consideration
ambient space, and construct a low-dimensional representation using a cost function that retains local properties of the data; they can be viewed as defining
Dimensionality_reduction
Unit of measurement
product) provides to a user. Function points are used to compute a functional size measurement (FSM) of software. The cost (in dollars or hours) of a single
Function_point
Cost Function (because of the duality between cost and production functions, a specific technology can be represented equally well by either the cost
List_of_production_functions
Machine learning technique
algorithms. That is, algorithms that optimize a cost function over function space by iteratively choosing a function (weak hypothesis) that points in the negative
Gradient_boosting
Graph data structure
joins and is worst-case optimal. Given an e-class and a cost function that maps each function symbol in Σ {\displaystyle \Sigma } to a natural number
E-graph
Hypothesis in neuroscience
equations. In contrast, optimal control optimizes the flow, given a cost function, under the assumption that W=0 (i.e., the flow is curl free or has detailed
Free_energy_principle
Information-theoretic measure
cross-entropy is given by ek=H(p,qk)−λK∑j≠kH(qj,qk) where ek is the cost function of the kth classifier, qk is the output probability of the kth classifier
Cross-entropy
Procedures to optimize practices in cost efficient ways
relationship to products, business functions, production volume, controllability, timing, and managerial decisions. Basic cost elements include materials and
Cost_accounting
Concept in probability theory
distance (or half the norm) arises as the optimal transportation cost, when the cost function is c ( x , y ) = 1 x ≠ y {\displaystyle c(x,y)={\mathbf {1} }_{x\neq
Total variation distance of probability measures
Total_variation_distance_of_probability_measures
Subfield of machine learning, intelligent control, and control theory
may also identify arbitrary nonlinear control laws which minimize the cost function of the plant. In this case, neither a model, the control law structure
Machine_learning_control
the overall cost incurred due to processing the tasks with respect to the states and due to the cost to change states. If the cost function to change states
Metrical_task_system
Computational model used in machine learning
constant and the cost C=E[(x−f(x))2]. Minimizing this cost produces a value of a that is equal to the mean of the data. The cost function can be much more
Neural network (machine learning)
Neural_network_(machine_learning)
Set of methods for supervised statistical learning
described above) depends only on a subset of the training data, because the cost function for building the model does not care about training points that lie
Support_vector_machine
resulting controller is only optimal with respect to the prescribed cost function and does not necessarily represent the best controller in terms of the
H-infinity methods in control theory
H-infinity_methods_in_control_theory
Quantum algorithm
to other optimization problems by adapting the Hamiltonian to be a cost function. The choice of ansatz state depends on the system of interest. In gate-based
Variational quantum eigensolver
Variational_quantum_eigensolver
Part of an activity that causes the change in its cost
Porter's approach defines a "cost driver" not just as a simple variable in a function, but as something that changes the function itself. For example, the
Cost_driver
Feature to efficiently execute queries efficiently in DBMS software
associates each query plan with a cost function that maps from a multi-dimensional parameter space to a one-dimensional cost space. The goal of optimization
Query_optimization
String metric for measuring edit distance
weighted edit distance is not automatically a metric for arbitrary cost functions; metric properties depend on the conditions imposed on those costs.
Levenshtein_distance
Operations related to the reuse of products and materials
flow of goods. Objective function: minimizing linear cost function incorporating fix cost of settling sites and transportation cost of returning goods Decision
Reverse logistics network modelling
Reverse_logistics_network_modelling
Systematic approach to estimating the strengths and weaknesses of alternatives
Cost–benefit analysis (CBA), sometimes also called benefit–cost analysis, is a systematic approach to estimating the strengths and weaknesses of alternatives
Cost–benefit_analysis
Unrecoverable cost that has been incurred
In economics and business decision-making, a sunk cost (also known as retrospective cost) is a cost that has already been incurred and cannot be recovered
Sunk_cost
Concept in economics
revenue equals marginal cost (MC). To derive MC the first derivative of the total cost function is taken. For example, assume cost, C, equals 420 + 60Q +
Demand
Mathematical transformation
function of price, profit max ( P ) {\displaystyle {\text{profit}}_{\text{max}}(P)} , we see that it is the Legendre transform of the cost function C
Legendre_transformation
Image reconstruction algorithms
is more widely used. A cost function that is to be minimized to estimate the image coefficient vector. Often this cost function includes some form of regularization
Iterative_reconstruction
Concept in linear programming and mathematical optimization
In linear programming, reduced cost, or opportunity cost, is the amount by which an objective function coefficient would have to improve (so increase
Reduced_cost
Technique to make a model more generalizable and transferable
problems. The regularization term, or penalty, imposes a cost on the optimization function to make the optimal solution unique. Implicit regularization
Regularization_(mathematics)
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