We introduce a convex optimization modeling framework that transforms a convex optimization problem expressed in a form natural and convenient for the user into an equivalent cone program in a way that preserves fast linear transforms in the original problem. By representing linear functions in the transformation process not as matrices, but as graphs that encode composition of linear operators...

For a non-Archimedean locally convex space (E, τ), the finest locally convex topology having the same as τ convergent sequences and the finest locally convex topology having the same as τ compactoid sets are studied.

In this paper, we consider a type of cone-constrained convex program in finitedimensional space, and are interested in characterization of the solution set of this convex program with the help of the Lagrange multiplier. We establish necessary conditions for a feasible point being an optimal solution. Moreover, some necessary conditions and sufficient conditions are established which simplifies...

We introduce a new class of cooperative games by using the notion of local supermodularity. Therefore locally convex games can be considered as relaxations of convex games. Moreover, we obtain a characterization of a subclass of locally concave games in terms of the rank function of a matroid.

We introduce a new class of cooperative games by using the notion of local supermodularity. Therefore locally convex games can be considered as relaxations of convex games. Cooperative games with the unit marginal worth property are defined and characterizations of locally concave (convex) games with this property are proved. Moreover, we obtain a characterization of a subclass of locally conca...