General convex optimization problem

  • Is convex optimization a generalization of linear programming?

    Convex optimization is a generalization of linear programming where the constraints and objective function are convex.
    Both the least square problems and linear programming is a special case of convex optimization..

Overview

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets(or, …

Definition

A convex optimization problem is an optimization problem in which the objective function is a convex function and the feasible set is a convex set. A f…

Applications

The following problem classes are all convex optimization problems, or can be reduced to convex optimization problems via simple transformations:

Lagrange multipliers

Consider a convex minimization problem given in standard form by a cost function and inequality constraints for . Then the dom…

Algorithms

Unconstrained convex optimization can be easily solved with gradient descent (a special case of steepest descent) or Newton's method, combin…


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