Second-order cone programming (SOCP) is a type of convex optimization problem where the objective function is linear and the feasible region is defined by second-order cones. These cones consist of vectors that represent a combination of quadratic constraints and linear inequalities, allowing for a wide range of applications in fields such as control theory, finance, and engineering. This structure is essential in understanding the properties of convex cones, particularly how they can be utilized to form and solve optimization problems efficiently.
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