Robust optimization is a distinct approach to optimizations problems that allows for the incorporation of
uncertainty. The usefulness of robust optimization lies in the ability to solve for every realization of the uncertain
parameters. As a result, the problem can be solved for the worst-case scenarios of the entire set...
The chance-constrained method is one of the major approaches to solving optimization problems under various
uncertainties. It is a formulation of an optimization problem that ensures that the probability of meeting a certain
constraint is above a certain level. In other words, it restricts the feasible region so that the...
Quadratic programming (QP) is the
problem of optimizing a quadratic
objective function and is one of the
simplests form of non-linear
programming. The objective function
can contain bilinear or up to second
order polynomial terms, and the
constraints are linear and can be both
equalities and inequalities. QP is
widely...
Sigmoid problems are a class of optimization problems with the objective of maximizing the sum of multiple
sigmoid functions. They are defined by their limits at negative and positive infinity. Similar to the unit step
function the function approaches 1 as it approaches infinity and approaches -1 as it approaches...
Column generation algorithms are used for MILP problems. The formulation was initially proposed by Ford and
Fulkerson in 1958 . The main advantage of column generation is that not all possibilities need to be enumerated.
Instead, the problem is first formulated as a restricted master problem (RMP). This RMP has...
Optimization with absolute values is a special case of linear programming in which a problem made nonlinear due
to the presence of absolute values is solved using linear programming methods.
Absolute value functions themselves are very difficult to perform standard optimization procedures on. They are
not continuously differentiable functions, are...
Computational complexity refers to the amount of resources
required to solve a type of problem by systematic application of an
algorithm. Resources that can be considered include the amount of
communications, gates in a circuit, or the number of processors.
Because the size of the particular input to a problem...