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GPOPS-II [3] is designed to solve multiple-phase optimal control problems of the following mathematical form (where is the number of phases): = ((), …, ()) subject to the dynamic constraints
The mixed complementarity problem is defined by a mapping ():, lower values {} and upper values {}, with {, …,}. The solution of the MCP is a vector x ∈ R n {\displaystyle x\in \mathbb {R} ^{n}} such that for each index i ∈ { 1 , … , n } {\displaystyle i\in \{1,\ldots ,n\}} one of the following alternatives holds:
Mixed-radix numbers of the same base can be manipulated using a generalization of manual arithmetic algorithms. Conversion of values from one mixed base to another is easily accomplished by first converting the place values of the one system into the other, and then applying the digits from the one system against these.
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers.In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear.
This problem is also classified as NP-hard, and in fact the decision version was one of Karp's 21 NP-complete problems. If only some of the unknown variables are required to be integers, then the problem is called a mixed integer (linear) programming (MIP or MILP) problem. These are generally also NP-hard because they are even more general than ...
Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions.Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constraints on the variables.