Journal:Informatica
Volume 27, Issue 4 (2016), pp. 799–818
Abstract
We present an algorithm to solve multistage stochastic convex problems, whose objective function and constraints are nonlinear. It is based on the twin-node-family concept involved in the Branch-and-Fix Coordination method. These problems have 0–1 mixed-integer and continuous variables in all the stages. The non-anticipativity constraints are satisfied by means of the twin-node-family strategy.
In this work to solve each nonlinear convex subproblem at each node we propose the solution of sequences of quadratic subproblems. Due to the convexity of the constraints we can approximate them by means of outer approximations. These methods have been implemented in C++ with the help of CPLEX 12.1, which only solves the quadratic approximations. The test problems have been randomly generated by using a C++ code developed by this author. Numerical experiments have been performed and its efficiency has been compared with that of a well-known code.
Journal:Informatica
Volume 20, Issue 2 (2009), pp. 203–216
Abstract
One of the most known applications of Discrete Optimization is on scheduling. In contrast, one of the most known applications of Continuous Nonlinear Optimization is on the control of dynamic systems. In this paper, we combine both views, solving scheduling problems as dynamic systems, modeled as discrete-time nonlinear optimal control problems with state and control continuous variables subjected to upper and lower bounds. Complementarity constraints are used to represent scheduling decisions. One example we discuss in detail is the crude oil scheduling in ports, with numerical results presented.
Journal:Informatica
Volume 1, Issue 1 (1990), pp. 40–58
Abstract
A new concept of an exact auxiliary function (EAF) is introduced. A function is said to be EAF, if the set of global minimizers of this function coincides with the global solution set of the initial optimization problem. Sufficient conditions for exact equivalence of the constrained minimization problem and minimization of EAF are provided. The paper presents various classes of EAF for a non linear programming problem, which has a saddle point of Lagra ge function.