The multiobjective bilevel program is a sequence of two optimization problems where the upper level problem is multiobjective and the constraint region of the upper level problem is determined implicitly by the solution set to the lower level problem. In the case where the Karush-Kuhn-Tucker (KKT) condition is necessary and sufficient for global optimality of … Read more
Computational noise in deterministic simulations is as ill-defined a concept as can be found in scientific computing. When coupled with adaptive strategies, the effects of finite precision destroy smoothness of the simulation output and complicate subsequent analysis. Following the work of Hamming on roundoff errors, we present a new algorithm, ECnoise, for quantifying the noise … Read more
The number of dual-career couples with children is growing fast. These couples face various challenging problems of organizing their lifes, in particular connected with childcare and time-management. As a typical example we study one of the difficult decision problems of a dual career couple from the point of view of operations research with a particular … Read more
We consider optimization of nonlinear objective functions that balance $d$ linear criteria over $n$-element independence systems presented by linear-optimization oracles. For $d=1$, we have previously shown that an $r$-best approximate solution can be found in polynomial time. Here, using an extended Erdos-Ko-Rado theorem of Frankl, we show that for $d=2$, finding a $\rho n$-best solution … Read more
We introduce the concept of a Markov risk measure and we use it to formulate risk-averse control problems for two Markov decision models: a finite horizon model and a discounted infinite horizon model. For both models we derive risk-averse dynamic programming equations and a value iteration method. For the infinite horizon problem we also develop … Read more
We address an optimization problem in which two agents, each with a set of weighted items, compete in order to maximize the total weight of their winning sets. The latter are built according to a sequential game consisting in a fixed number of rounds. In every round each agent submits one item for possible inclusion … Read more
This paper studies the vector optimization problem of finding weakly ef- ficient points for maps from Rn to Rm, with respect to the partial order induced by a closed, convex, and pointed cone C ⊂ Rm, with nonempty inte- rior. We develop for this problem an extension of the proximal point method for scalar-valued convex … Read more
In 2004, Graña Drummond and Iusem proposed an extension of the projected gradient method for constrained vector optimization problems. In that method, an Armijo-like rule, implemented with a backtracking procedure, was used in order to determine the steplengths. The authors just showed stationarity of all cluster points and, for another version of the algorithm (with … Read more
In this paper, we analyze and characterize the cone of nonsymmetric positive semidefinite matrices (NS-psd). Firstly, we study basic properties of the geometry of the NS-psd cone and show that it is a hyperbolic but not homogeneous cone. Secondly, we prove that the NS-psd cone is a maximal convex subcone of $P_0$-matrix cone which is … Read more
Bargaining is a basic game in economic practice. Cournot duopoly game is an important model in bargaining theory. Recently, asymmetry information [20] and incomplete information [19], limited individual rationality [2] and slightly altruistic equilibrium [10] are introduced into bargaining theory. And computational game theory come into being a new research field. In this paper, we … Read more