Characterizations of metric projections in Banach spaces and applications.
Characterizations of the Solution Sets of Generalized Convex Minimization Problems
2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20.In this paper we obtain some simple characterizations of the solution sets of a pseudoconvex program and a variational inequality. Similar characterizations of the solution set of a quasiconvex quadratic program are derived. Applications of these characterizations are given.
Characterizations of ɛ-duality gap statements for constrained optimization problems
In this paper we present different regularity conditions that equivalently characterize various ɛ-duality gap statements (with ɛ ≥ 0) for constrained optimization problems and their Lagrange and Fenchel-Lagrange duals in separated locally convex spaces, respectively. These regularity conditions are formulated by using epigraphs and ɛ-subdifferentials. When ɛ = 0 we rediscover recent results on stable strong and total duality and zero duality gap from the literature.
Characterizing Optimality in Nonconvex Optimization: Addendum
Characterizing Optimality in Nonconvex Optimizationi
Chemins extrémaux d'un graphe doublement valué
Clasificación en programación multiobjetivo.
En el presente trabajo, después de justificar lo importante que resulta para el decisor, en muchos casos, el poder obtener clasificaciones en el conjunto de objetivos de un problema de Porgramación Multiobjetivo, se hace un estudio algorítmico que permite agruparlos en función de ciertos niveles de conformidad.
Classical hierarchies form a modern standpoint. Part III. BP-sets
Clique partitioning of interval graphs with submodular costs on the cliques
Given a graph G = (V,E) and a “cost function” (provided by an oracle), the problem [PCliqW] consists in finding a partition into cliques of V(G) of minimum cost. Here, the cost of a partition is the sum of the costs of the cliques in the partition. We provide a polynomial time dynamic program for the case where G is an interval graph and f belongs to a subclass of submodular set functions, which we call “value-polymatroidal”. This provides a common solution for various generalizations of the...
Clique-connecting forest and stable set polytopes
Let G = (V,E) be a simple undirected graph. A forest F ⊆ E of G is said to be clique-connecting if each tree of F spans a clique of G. This paper adresses the clique-connecting forest polytope. First we give a formulation and a polynomial time separation algorithm. Then we show that the nontrivial nondegenerate facets of the stable set polytope are facets of the clique-connecting polytope. Finally we introduce a family of rank inequalities which are facets, and which generalize the clique inequalities. ...
Closedness of the solution mapping to parametric vector equilibrium problems.
Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators
In this note we provide regularity conditions of closedness type which guarantee some surjectivity results concerning the sum of two maximal monotone operators by using representative functions. The first regularity condition we give guarantees the surjectivity of the monotone operator S(· + p) + T(·), where p ɛ X and S and T are maximal monotone operators on the reflexive Banach space X. Then, this is used to obtain sufficient conditions for the surjectivity of S + T and for the situation when...
Codimension one minimal projections in Banach spaces and a mathematical programming problem [Book]
Codings and operators in two genetic algorithms for the leaf-constrained minimum spanning tree problem
The features of an evolutionary algorithm that most determine its performance are the coding by which its chromosomes represent candidate solutions to its target problem and the operators that act on that coding. Also, when a problem involves constraints, a coding that represents only valid solutions and operators that preserve that validity represent a smaller search space and result in a more effective search. Two genetic algorithms for the leaf-constrained minimum spanning tree problem illustrate...
Coercivity properties and well-posedness in vector optimization
This paper studies the issue of well-posedness for vector optimization. It is shown that coercivity implies well-posedness without any convexity assumptions on problem data. For convex vector optimization problems, solution sets of such problems are non-convex in general, but they are highly structured. By exploring such structures carefully via convex analysis, we are able to obtain a number of positive results, including a criterion for well-posedness in terms of that of associated scalar problems....
Coercivity properties and well-posedness in vector optimization*
This paper studies the issue of well-posedness for vector optimization. It is shown that coercivity implies well-posedness without any convexity assumptions on problem data. For convex vector optimization problems, solution sets of such problems are non-convex in general, but they are highly structured. By exploring such structures carefully via convex analysis, we are able to obtain a number of positive results, including a criterion for well-posedness in terms of that of associated scalar...
Cœur et nucléolus des jeux de recouvrement
Coeur et nucléolus des jeux de recouvrement
A cooperative game is defined as a set of players and a cost function. The distribution of the whole cost between the players can be done using the core concept, that is the set of all undominated cost allocations which prevent players from grouping. In this paper we study a game whose cost function comes from the optimal solution of a linear integer covering problem. We give necessary and sufficient conditions for the core to be nonempty and characterize its allocations using linear programming...
Coevolutionary genetic algorithms for establishing Nash equilibrium in symmetric Cournot games.
Colored decision process Petri nets: modeling, analysis and stability
In this paper we introduce a new modeling paradigm for developing a decision process representation called the Colored Decision Process Petri Net (CDPPN). It extends the Colored Petri Net (CPN) theoretic approach including Markov decision processes. CPNs are used for process representation taking advantage of the formal semantic and the graphical display. A Markov decision process is utilized as a tool for trajectory planning via a utility function. The main point of the CDPPN is its ability to...