Convex optimization vs linear programming

×Convex optimization is a type of optimization that involves minimizing a convex objective function (or maximizing a concave objective function) over a convex set of constraints. Linear programming is a special case of convex optimization where the objective function is linear and the constraints consist of linear equalities and inequalities. Linear programs and convex quadratic programs are convex optimization problems. Since any linear program is a convex optimization problem, we can consider convex optimization to be a generalization of linear programming.,Convex optimization involves minimizing a convex objective function (or maximizing a concave objective function) over a convex set of constraints. Linear programming is a special case of convex optimization where the objective function is linear and the constraints consist of linear equalities and inequalities.A typical definition is that convex optimization asks for best value of a convex function over a convex set, and by that definition linear programs are convex optimization problems.Linear programs (LP) and convex quadratic programs (QP) are convex optimization problems. Conic optimization problems, where the inequality constraints are convex cones, are also convex optimization problems.Since any linear program is therefore a convex optimization problem, we can consider convex optimization to be a generalization of linear programming. An optimization problem is called linear, if the objective and constraint functions are all linear, i.e. satisfy