Optimization” and “Optimum” redirect here. Many real-world and theoretical problems may be modeled in this general framework. In mathematics, conventional optimization problems are boyd vandenberghe convex optimization pdf stated in terms of minimization. Local maxima are defined similarly.
A large number of algorithms proposed for solving nonconvex problems—including the majority of commercially available solvers—are not capable of making a distinction between locally optimal solutions and globally optimal solutions, and will treat the former as actual solutions to the original problem. Optimization problems are often expressed with special notation. Dantzig studied at that time. This can be viewed as a particular case of nonlinear programming or as generalization of linear or convex quadratic programming.
It is a generalization of linear and convex quadratic programming. LP, SOCP and SDP can all be viewed as conic programs with the appropriate type of cone. This is not convex, and in general much more difficult than regular linear programming. For specific forms of the quadratic term, this is a type of convex programming. The special class of concave fractional programs can be transformed to a convex optimization problem.