More details about fmincon can be found at MATLAB documentation. fminconįmincon is a MATLAB function for finding the minimum of finite-dimensional constrained optimization problem. COCO constructors are used to generating (discretized) constrained optimization problems, which are then solved using fmincon in MATLAB. Here, we provide an alternative for solving constrained optimization problems. The necessary conditions are often given in the form of bvps, which can be solved using successive continuation methods. Such adjoints can be used to formulate the first-order necessary conditions to constrained optimization problems. Further, COCO provides constructors for the adjoint operators of these problems. Specifically, it has constructors for collocation problems (coll), boundary value problems (bvp), periodic orbit problems (po) and hybrid system periodic orbit problems (hspo). This object-oriented construction paradigm enables us to build a composite problem from building blocks.ĬOCO provides a predefined library for the building blocks. It supports the detection of bifurcation points on solution manifolds and the switch from one solution branch to the other.Ī unique feature of COCO is the embedded construction philosophy of nonlinear systems, where a large problem is assembled by small subproblems with weak couplings. It uses atlas algorithms to cover the solution manifolds of nonlinear systems. Plot(N,lsq.Residual, 'k',N,lsqfd.Residual, 'b-',N,fmin.Residual, 'g',N,fminfd.COCO wrapper functions for fmincon in MATLAB COCOĬontinuation Core (COCO) is a MATLAB-based open-source package for computational nonlinear analysis of dynamical systems. Semilogy(N,lsq.Fcount, 'k',N,lsqfd.Fcount, 'b-',N,fmin.Fcount, 'g',N,fminfd.Fcount, 'r-') Legend( 'lsqnonlin', 'lsqnonlin FD', 'fmincon', 'fmincon FD', 'Location', 'northwest') Plot(N,lsq.Iterations, 'k',N,lsqfd.Iterations, 'b-',N,fmin.Iterations, 'g',N,fminfd.Iterations, 'r-') = solve(prob,x0,Options=optsfmincon,Solver= "fmincon". = solve(prob,x0,Options=optsfmincon,Solver= "fmincon") ObjectiveDerivative= 'finite-differences',ConstraintDerivative= 'finite-differences') % Include a set of nonlinear inequality constraintsĬons(i) = x(i)^2 + y(i)^2 <= 1/2 + 1/8*i Y = optimvar( "y",N,LowerBound=0,UpperBound=9) X = optimvar( "x",N,LowerBound=-3,UpperBound=3) Lsq = struct( 'Iterations',z, 'Fcount',z, 'Residual',z) MaxFunctionEvaluations=1e5,MaxIterations=1e4) Optsfmincon = optimoptions( "fmincon",Display= "none". MaxFunctionEvaluations=1e5,MaxIterations=1e4) % Allow for many iterations and Fevals Optslsq = optimoptions( "lsqnonlin",Display= "none". The function also plots the results, showing:įunction = runlsqfmincon() For a description of the Rosenbrock function, see Solve a Constrained Nonlinear Problem, Problem-Based. The runlsqfmincon helper function listed at the end of this example creates a series of scaled Rosenbrock-type problems with nonlinear constraints for N ranging from 1 to 50, where the number of problem variables is 2 N. In other words, fmincon can access only the value of the sum, but lsqnonlin can access each component separately. In contrast, lsqnonlin works with the entire vector F, meaning it has access to all the components of the sum. fmincon minimizes the sum of squares given as ∑ i F i 2, where F is a vector function. The reason is that lsqnonlin has more information to work with. Yet lsqnonlin typically solves problems in fewer function evaluations. Both solvers use the fmincon 'interior-point' algorithm for solving the problem. This example shows that lsqnonlin generally takes fewer function evaluations than fmincon when solving constrained least-squares problems.
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