Release with many small fixes as two years have passed since the last official update.

Main fixes and additions

• Added support for global nonlinear optimization framework in GUROBI
• Full LP warm-starts in optimizer when using Gurobi now supported thanks to contributions from Tom Holden
• Updates for recent versions of LINPROG

Release with new and improved solver support, and some minor fixes.

Main fixes and additions

• Added support for COPT, thanks to the LEAVES group, RIIS at Shanghai University of Finance and Economics
• Updated support for KNITRO 13.2
• Updated support for XPRESS 9.0
• KKT now supports nonlinearly parameterized models
• Massive performance improvement on large sparse polynomial objectives in nonlinear solvers due to faster gradient computation
• Fixed bug which caused gradient information to be incorrect when EXPCONE models are solved with general nonlinear solvers
• The options bnb.plot and bmibnb.plot now mean the same thing (graphical view of lower/upper bound and stack information)
• Some minor issues which caused issues when upgrading from 2021-verion

Note that you have to install both the solver, and the MATLAB interface to the solver.

Untangling this from YALMIP is simple. Unboundedness can only come from the objective, hence remove the objective from the model and try again. If the message changes to Infeasible you know the model is infeasible and should start addressing that. If the solver instead solves the problem when the objective was removed, you know the model is unbounded, and should address that problem.

How to analyze a model for infeasibility is explained in the post debugging infeasible models. In short, remove constraints systematically until it becomes infeasible and you know where the peroblem lies, or add slacks to model and see which are activated.

How to analyze a model for unboundedness is explained in the post debugging unbounded models. In short, add large bounds on all variables (or small penalties) to make the model bounded, and see which variables become large when that problem is solved.

Release with possibly breaking core changes, new features, and 2 years of bug fixes.

Main fixes and additions

• Strict inequalities now trigger errors (no more kittens).
• Square symmetric inequalities now trigger warnings (detects extremely common user mistake).
• A bunch of old obsolete solvers removed and are no longer supported.
• @araujoms improved support for complex cones via sedumi in automatic dualization.
• BMIBNB improvements both algoritmically and performance.
• BNB cleaned up bug fixes (memory hogging) and improved performance for some models (more on that later in separate post).
• GUROBI options structure now up to date.
• DAQP added as supported solver.
• yalmiptest cleaned up and improved.
• Added some geometric operators such as vertex, isoutside, starpolygon.
• Experimental (pre-alpha) support of nonlinear semidefinite programming (more on that later in separate post).
• Option ‘usex0’ should be updated to ‘warmstart’ (both supported for now)
• Code fixed to support Octave 8.

Syntax

Model = isoutside(P)

Example

The following code finds the vertex/point on facet closest to the origin in a polytope by solving a non-convex problem involving an avoidance constraint. Note the required explicit bounds, as the model is constructed using big-M strategies.

x = sdpvar(2,1);
A = randn(10,2);
b = 10*rand(10,1);

Model = isoutside(A*x <= b)

optimize([Model, -100 <= x <= 100],x'*x)
clf
plot(A*x <= b,[],[],[],sdpsettings('plot.shade',0.1));
hold on;grid on
plot(value(x(1)),value(x(2)),'*')
r = sqrt(value(x'*x));
t = 0:0.01:2*pi;
plot(r*cos(t),r*sin(t),'--')

Comments

Note that isoutside will introduce binary variables.

Syntax

y = invpos(x)

Comments

The operator is implemented using a graph representation based on SOCP and can thus only be used in scenarios where YALMIP can propagate convexity and use a conic model.

Syntax

P = polytope(v,x)
P = polytope(M)

Example

The native YALMIP use is for defing a polytope \(x = \sum_{i=1}^N \lambda_i v_i, \lambda \geq 0, \sum_{i=1}^N \lambda_i = 1\) from a set of vertices \( v_i\).

v = randn(2,10);
x = sdpvar(2,1);
P = polytope(v,x)

The opeprator does not perform any convex hull computation to reduce the numer of vertices. Note also that the polytope is defined in the \(x,\lambda\)-space. Hence, if you want plot it, you are most likely interested in the projection to \(x\)

plot(P,x)

The command also serves as the interface between YALMIP objects and MPT objects, allow us to convert objects. To generate a polytopic MPT object, simply apply the operator on a purely linear object.

x = sdpvar(2,1);
P = polytope([-1 <= x <= 1]);