Summary of convex optimization knowledge points

Convex optimization Overview First, what is convex optimization

Not strictly speaking, the convex optimization is in the scope of the standard optimization problem, the requirement of objective function and constraint function is a kind of optimization problem of convex function. second, the importance

Convex optimization is so important because:
1. Its application is very extensive, many optimization problems in machine learning should be solved by convex optimization;
2. In the non-convex optimization, the convex optimization also plays an important role, many non-convex optimization problems, can be converted to convex optimization problem to solve;
3. As mentioned above, convex optimization problem can be considered as a problem with mature solution, while other optimization problems are not necessarily.
three, convex optimization knowledge system

1. Convex set, define the target function and the definition field of the constraint function.
2. Convex function, define the convexity limit of the optimization correlation function.
3. Convex optimization, the standard description of the central content.
4. Convex optimization problem solving, the core content, mainly is unconstrained optimization, equality constrained optimization, inequality constrained optimization. Correlation algorithm, Gradient descent method, Newton method, interior point method and so on.
5. Duality problem, it is an effective method to transform the general optimization problem into convex optimization problem and solve the convex optimization problem.
Iv. Standard Optimization issues

Five, convex optimization problem

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