mixed-integer monotonic programmingbranch-and-cutsurrogate Lagrangian relaxationMany important integer and mixed-integer programming problems are difficult to solve. A representative example is unit commitment with combined cycle units and transmission capacity constraints. Complicated transitions within combined ...
Mixed integer programming problems are defined as those where some or all of the decision variables are only allowed to be integers. This is typically required in a range of real world applications in allocation and planning problems where the discrete variables represent quantities, such as the nu...
Mixed-integer problems are those that involve both continuous and integer variables. The introduction of integer variables allows the modeling of complex decisions through graph theoretic representations denoted assuperstructures(Floudas, 1995). This representation leads to the simultaneous determination of the...
For MILFP Problems Objective: maximize(x∗ax∗b) where $x$ is variables and a, b are matrices. This ratio can be used to represent efficiency. For a Mixed Integer Linear Fractional Problem (MILFP), you may try to implement Charnes-Cooper tansformation which can convert a MILFP proble...
Mixed-integer nonlinear programming (MINLP) problems involving general constraints and objective functions with continuous and integer variables occur frequently in engineering design, chemical process industry and management. Although many optimization approaches have been developed for MINLP problems, these ...
Load the data for the problem. This data has 225 expected returns in the vectorrand the covariance of the returns in the 225-by-225 matrixQ. The data is the same as in the Using Quadratic Programming on Portfolio Optimization Problems example. ...
(MIQP) portfolio optimization problem using the problem-based approach. The idea is to iteratively solve a sequence of mixed-integer linear programming (MILP) problems that locally approximate the MIQP problem. For the solver-based approach, seeMixed-Integer Quadratic Programming Portfolio Optimization:...
Mixed Integer Linear Programming problems are generally solved using a linear-programming based branch-and-bound algorithm. Overview Basic LP-based branch-and-bound can be described as follows. We begin with the original MIP. Not knowing how to solve this problem directly, we remove all of the ...
DSP is an open-source and parallel package that implements decomposition methods for structured mixed-integer programming problems. These are structured optimization problems in the following form: minimize c^T x + \sum_{s=1}^S q_s^T y_s subject to A x = b T_s x + W_s y_s = h...
ever, different from stochastic programming, which is in a monolithic form, the two-stage RO is actually a tri-level optimization model that is very challenging to compute. Even a simple formulation with linear programming (LP) problems in both stages could be NP- ...