Convex problems, classifiers

Time is fast; I think of a report on the convex problem made by Nankai classmate last year.

The following is a friend of the letter written, paste it over with ^_^:

The general expression of the optimization problem in mathematics is to get, that is, the n-dimensional vector, the feasible domain, is the real value function on.

The convex set refers to any two points in the set, that is, any two points of the connected segments are in the collection, visually, the collection will not be like that there is "concave down" part. As for closed convex sets, it is related to the definition of closed set, and the definition of closed set is based on open set, compare abstract, do not repeat, here you can simply think that the closed convex set refers to the convex set containing all the boundary points.

A convex function refers to any two points in a defined field, which, intuitively, is a downward projection, as shown in the schematic.

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In the actual modeling, judging an optimization problem is not a convex optimization problem generally see the following points:

• The objective function is not a convex optimization problem if it is not a convex function
• The decision variable contains discrete variables (0-1 variables or integer variables), it is not a convex optimization problem
• When a constraint is written, it is not a convex optimization problem if it is not a convex function

The reason for distinguishing convex and non-convex problems is that local optimal solutions are also global optimal solutions in convex optimization problems, which makes convex optimization problems easier to solve in a certain sense, while general non-convex optimization problems are more difficult to solve.

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Looking at the above, I personally think that the so-called convex optimization problem seems to be explained by the question of high school linear programming. For example, the optimal solution of linear programming should be the solution of this convex optimization problem.

Here's what you'll want to know:

Another problem is the naive Bayesian classifier. The main problem to solve is P (c| D) this conditional probability. C represents the category, and D represents the document. The expression means that we want to calculate the probability that the observed document D determines that it belongs to category C. The effect of Bayesian is reflected by the calculation of the probability of direct calculation. The strong point is that the prior probability and the posterior probability can be converted to each other. P (c| D) =p (d| c) P (c)/P (D), through the training of the sample, we can estimate the P (d| by the assumption of the bag of words) c), you can also count P (c), the denominator is the same for all categories, and therefore can be ignored. In this way, we can divide the document D into a Class C with the most probability, and complete the classification of document D.

In addition, the research problem can not always be separated from the consumer preference theory: completeness, transmission, choice, superiority, continuous

Production potential boundary how to play a role in determining the best combination of production, and budget line and utility curve in a picture, the three points of tangency is the most advantage-at this time, under a certain budget constraints, a, b of the production substitution rate is equal to its price inverse ratio, the utility is also equal to the inverse price, in this point the consumer utility maximization Optimization of the producer production portfolio.

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Convex problems, classifiers