This paper is devoted to sequential decision problems with imprecise probabilities. We study the problem of determining an optimal strategy according to the Hurwicz criterion in decision trees. More precisely, we investigate this problem from the computational viewpoint. When the decision tree is separable (to be defined in the paper), we provide an operational approach to compute an optimal st...

An exact semidefinite linear programming (SDP) relaxation of a nonlinear semidefinite programming problem is a highly desirable feature because a semidefinite linear programming problem can efficiently be solved. This paper addresses the basic issue of which nonlinear semidefinite programming problems possess exact SDP relaxations under a constraint qualification. We do this by establishing exa...

in this paper, we will give necessary and sufficient conditions for certain hnnextensions of subgroup separable groups with normal associated subgroup to be conjugacyseparable. in fact, we will show that these hnn extensions are conjugacy separable if and onlyif the normalizer of one of its associated subgroup is conjugacy separable.

This paper proposed a novel classification model which introduced the kernel function into the original Multiple Criteria Linear Programming (MCLP) model. MCLP model is used as a classification method which can only solve linear separable problems in data mining. However, the proposed kernel-based MCLP model can deal with non-linear cases. Meanwhile, unlike some other complicated models, this m...

The paper deals with a flow distribution problem with a piecewise-linear cost function. The problem is formulated as a piecewise-linear programming problem which is not separable with respect to separate variable group. The method for solving this problem is based on the extension of the idea of the simplex method to the class of non-separable piecewise-linear problems. It secures finding of a ...

In this paper, we consider the problem of minimizing a strictly convex separable function over a feasible region defined by a convex inequality constraint and two-sided bounds on the variables (box constraints). Also, the convex separable program with a strictly convex objective function subject to linear equality constraints and bounded variables is considered. These problems are interesting f...

We propose the use of sequences of separable, piecewise linear approximations for solving nondifferentiable stochastic optimization problems. The approximations are constructed adaptively using a combination of stochastic subgradient information and possibly sample information on the objective function itself. We prove the convergence of several versions of such methods when the objective funct...

In this paper, we presented a novel semi-supervised one-class classification algorithm which assumes that class is linearly separable from other elements. We proved theoretically that class is linearly separable if and only if it is maximal by probability within the sets with the same mean. Furthermore, we presented an algorithm for identifying such linearly separable class utilizing linear pro...

Geometric programming problem is a powerful tool for solving some special type non-linear programming problems. It has a wide range of applications in optimization and engineering for solving some complex optimization problems. Many applications of geometric programming are on engineering design problems where parameters are estimated using geometric programming. When the parameters in the prob...