Disciplined Convex Programming and CVX
Disciplined Convex Programming and CVX
Stephen Boyd Electrical Engineering Department
Stanford University
Convex Optimization, Boyd & Vandenberghe
Outline
? cone program solvers ? modeling systems ? disciplined convex programming ? CVX (CVXPY, Convex.jl)
Convex Optimization, Boyd & Vandenberghe
1
Cone program solvers
? LP solvers ? many, open source and commercial
? cone solvers ? each handles combinations of a subset of LP, SOCP, SDP, EXP cones ? open source: SDPT3, SeDuMi, CVXOPT, CSDP, ECOS, SCS, . . . ? commercial: Mosek, Gurobi, Cplex, . . .
? you'll write a basic cone solver later in the course
Convex Optimization, Boyd & Vandenberghe
2
Transforming problems to cone form
? lots of tricks for transforming a problem into an equivalent cone program ? introducing slack variables ? introducing new variables that upper bound expressions
? these tricks greatly extend the applicability of cone solvers ? writing code to carry out this transformation is painful ? modeling systems automate this step
Convex Optimization, Boyd & Vandenberghe
3
Modeling systems
a typical modeling system ? automates transformation to cone form; supports
? declaring optimization variables ? describing the objective function ? describing the constraints ? choosing (and configuring) the solver
? when given a problem instance, calls the solver
? interprets and returns the solver's status (optimal, infeasible, . . . )
? (when solved) transforms the solution back to original form
Convex Optimization, Boyd & Vandenberghe
4
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