The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated S-...
Our resulting relaxation does not use significantly more variables than the original problem, in contrast to many other relaxations based on lifting. The corresponding separation problem is a highly structured semidefinite program (SDP) with convex but non-smooth objective. We propose to solve this ...
Quadratic programming (QP) is minimizing or maximizing an objective function subject to bounds, linear equality, and inequality constraints. Example problems include portfolio optimization in finance, power generation optimization for electrical utilities, and design optimization in engineering. Quadratic progra...
Quadratic programming problems can also be convex problems, despite their non-linearity, as long as the objective function is quadratic (convex) and its constraints are affine. Such a problem may be represented as follows [29,75]: (7)minimize1/2xTPx+qTx (7a)subjecttoGx≤h (7b)Ax=b where...
For more information, see the LinearSolver option description and interior-point-convex quadprog Algorithm. Example: [2,1;1,3] Data Types: single | double f— Linear objective term real vector Linear objective term, specified as a real vector. f represents the linear term in the expression 1...
Check if any variables appear only as linear terms in the objective function and do not appear in any linear constraint. If so, check for feasibility and boundedness, and then fix the variables at their appropriate bounds. Change any linear inequality constraints to linear equality constraints by...
QP refers to the mathematical programming with the objective being a quadratic function of design variables and constraints being linear functions of design variables. The objective function is raised from the linear function of LP to the quadratic function. Compared with LP, the amount of solution ...
Note the important requirement that Q is symmetric positive semidefinite; otherwise the objective function would not be convex. 10.1.1 Geometry of quadratic optimization Quadratic optimization has a simple geometric interpretation; we minimize a convex quadratic function over a polyhedron., see Fig. ...
However, since the maximum-clique problem admits a reformulation in the form of (StQP) [34], this problem class is NP-hard. Therefore, we can view the class of StQP as the simplest of the hard problems: the simplest nonconvex objective functions are generated by indefinite Hessians, and ...
Optimization completed because the objective function is non-decreasing in feasible directions, to within the value of the optimality tolerance, and constraints are satisfied to within the value of the constraint tolerance. Elapsed time is 0.224405 seconds. Plot results. Get plotPortfDemoStandard...