scholarly journals Generating Efficient Outcome Points for Convex Multiobjective Programming Problems and Its Application to Convex Multiplicative Programming

2011 ◽  
Vol 2011 ◽  
pp. 1-21
Author(s):  
Le Quang Thuy ◽  
Nguyen Thi Bach Kim ◽  
Nguyen Tuan Thien
Keyword(s):  
Multiobjective Programming ◽  
Outer Approximation ◽  
Test Problems ◽  
Multiplicative Programming ◽  
Efficient Outcome ◽  
Bond Portfolio ◽  
Outcome Space ◽  
Outer Approximation Algorithm ◽  
Multiobjective Programming Problems ◽  
Convex Multiplicative Programming

Convex multiobjective programming problems and multiplicative programming problems have important applications in areas such as finance, economics, bond portfolio optimization, engineering, and other fields. This paper presents a quite easy algorithm for generating a number of efficient outcome solutions for convex multiobjective programming problems. As an application, we propose an outer approximation algorithm in the outcome space for solving the multiplicative convex program. The computational results are provided on several test problems.

Variants for the logarithmic-quadratic proximal point scalarization method for multiobjective programming

2018 ◽  
Vol 11 (06) ◽  
pp. 1850081
Author(s):  
Rómulo Castillo ◽  
Clavel Quintana
Keyword(s):  
Convex Functions ◽  
Multiobjective Programming ◽  
Proximal Point Method ◽  
Test Problems ◽  
Proximal Point ◽  
Pareto Solution ◽  
Positive Orthant ◽  
Scalarization Method ◽  
Weak Pareto Solution ◽  
Multiobjective Programming Problems

We consider the proximal point method for solving unconstrained multiobjective programming problems including two families of real convex functions, one of them defined on the positive orthant and used for modifying a variant of the logarithm-quadratic regularization introduced recently and the other for defining a family of scalar representations based on 0-coercive convex functions. We show convergent results, in particular, each limit point of the sequence generated by the method is a weak Pareto solution. Numerical results over fourteen test problems are shown, some of them with complicated pareto sets.

A Global Optimization Approach for Solving the D.C. Multiplicative Programming Problem

2013 ◽  
Vol 765-767 ◽  
pp. 1196-1199
Author(s):  
Xue Gang Zhou
Keyword(s):  
Global Optimization ◽  
Programming Problem ◽  
Outer Approximation ◽  
Convex Compact ◽  
Feasible Region ◽  
Optimization Approach ◽  
Auxiliary Variables ◽  
Global Optimization Algorithm ◽  
Multiplicative Programming ◽  
Outer Approximation Algorithm

In this paper, we present a global optimization algorithm for solving the D.C. multiplicative programming (DCMP) over a convex compact subset. By introducing auxiliary variables, we give a transformation under which both the objective and the feasible region turn to be d.c.Then we solve equivalent D.C. programming problem by branch and bound method and outer approximation algorithm.

scholarly journals Partially distributed outer approximation

2021 ◽  
Author(s):  
Alexander Murray ◽  
Timm Faulwasser ◽  
Veit Hagenmeyer ◽  
Mario E. Villanueva ◽  
Boris Houska
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Outer Approximation ◽  
Mixed Integer ◽  
Global Optimality ◽  
Integer Optimization ◽  
Global Minimizers ◽  
Outer Approximation Method ◽  
Coupling Constraints ◽  
Outer Approximation Algorithm

AbstractThis paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads and to mixed-integer regression.

Multiobjective Programming

2014 ◽  
pp. 1585-1604
Author(s):  
Minghe Sun
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Objective Functions ◽  
Solution Quality ◽  
Solution Methods ◽  
Multiobjective Programming Problem ◽  
Feasible Solutions ◽  
Multiobjective Programming Problems

Optimization problems with multiple criteria measuring solution quality can be modeled as multiobjective programming problems. Because the objective functions are usually in conflict, there is not a single feasible solution that can optimize all objective functions simultaneously. An optimal solution is one that is most preferred by the decision maker (DM) among all feasible solutions. An optimal solution must be nondominated but a multiobjective programming problem may have, possibly infinitely, many nondominated solutions. Therefore, tradeoffs must be made in searching for an optimal solution. Hence, the DM's preference information is elicited and used when a multiobjective programming problem is solved. The model, concepts and definitions of multiobjective programming are presented and solution methods are briefly discussed. Examples are used to demonstrate the concepts and solution methods. Graphics are used in these examples to facilitate understanding.

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