Optimization Techniques Quiz

Linear Programming: method to optimize a linear objective function, subject to linear constraints
- Uses: allocation of resources, production planning, and inventory management
- Key concepts: decision variables, objective function, constraints, and optimality conditions
Non-Linear Programming: method to optimize a non-linear objective function, subject to non-linear constraints
- Uses: portfolio optimization, and cost minimization
- Key concepts: KKT conditions, Lagrange multipliers, and gradient descent
Dynamic Programming: method to optimize a problem by breaking it down into smaller sub-problems
- Uses: resource allocation, and decision-making under uncertainty
- Key concepts: Bellman equation, value function, and policy function

Regression Analysis: method to establish a relationship between a dependent variable and one or more independent variables
- Uses: forecasting, hypothesis testing, and policy analysis
- Key concepts: ordinary least squares (OLS), coefficient of determination, and residual analysis
Time Series Analysis: method to analyze and forecast time-series data
- Uses: forecasting, and identifying patterns and trends
- Key concepts: autocorrelation, partial autocorrelation, and ARIMA models
Panel Data Analysis: method to analyze data with multiple variables and observations over time
- Uses: estimation of causal relationships, and policy evaluation
- Key concepts: fixed effects, random effects, and generalized method of moments (GMM)

Ordinary Differential Equations (ODEs): method to model dynamic systems with a continuous variable
- Uses: modeling population growth, and chemical reactions
- Key concepts: first-order and second-order ODEs, separation of variables, and linear stability analysis
Partial Differential Equations (PDEs): method to model dynamic systems with multiple variables
- Uses: modeling heat diffusion, and wave propagation
- Key concepts: first-order and second-order PDEs, boundary value problems, and Fourier analysis

Non-Cooperative Games: method to analyze strategic interactions between individuals or firms
- Uses: oligopoly theory, and auctions
- Key concepts: Nash equilibrium, Pareto optimality, and dominant strategy
Cooperative Games: method to analyze cooperative interactions between individuals or firms
- Uses: bargaining theory, and coalition formation
- Key concepts: core, Shapley value, and Nash bargaining solution
Evolutionary Game Theory: method to analyze the evolution of strategies over time
- Uses: modeling the evolution of cooperation, and altruism
- Key concepts: replicator dynamics, and evolutionary stability

Walrasian Equilibrium: method to analyze the equilibrium of multiple markets in an economy
- Uses: studying the behavior of markets, and the effects of policy changes
- Key concepts: excess demand, and the law of supply and demand
Arrow-Debreu Model: method to analyze the equilibrium of multiple markets with uncertainty
- Uses: studying the behavior of markets with uncertainty, and the effects of policy changes
- Key concepts: complete markets, and Pareto optimality
Computational General Equilibrium: method to analyze the equilibrium of multiple markets using computational models
- Uses: studying the behavior of markets, and the effects of policy changes
- Key concepts: numerical methods, and simulation analysis

Linear Programming is used for allocating resources, production planning, and inventory management, key concepts include decision variables, objective function, constraints, and optimality conditions
Non-Linear Programming is used for portfolio optimization and cost minimization, key concepts include KKT conditions, Lagrange multipliers, and gradient descent
Dynamic Programming is used for resource allocation and decision-making under uncertainty, key concepts include Bellman equation, value function, and policy function

Used for forecasting, hypothesis testing, and policy analysis
Key concepts include ordinary least squares (OLS), coefficient of determination, and residual analysis

Used for estimation of causal relationships and policy evaluation
Key concepts include fixed effects, random effects, and generalized method of moments (GMM)

Used for modeling population growth and chemical reactions
Key concepts include first-order and second-order ODEs, separation of variables, and linear stability analysis

Used for modeling heat diffusion and wave propagation
Key concepts include first-order and second-order PDEs, boundary value problems, and Fourier analysis

Used for studying the behavior of markets with uncertainty and the effects of policy changes
Key concepts include complete markets and Pareto optimality