Jorge R. Vera

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A conic linear system is a system of the form P(d) : find x that solves b− Ax ∈ CY , x ∈ CX , where CX and CY are closed convex cones, and the data for the system is d = (A, b). This system is“wellposed” to the extent that (small) changes in the data (A, b) do not alter the status of the system (the system remains solvable or not). Renegar defined the(More)
This paper describes a strategy for defining priorities for the branching variables in a Branch and Bound algorithm. The strategy is based on shape information about the polyhedron over which we are optimizing. This information is related to measures of the integer width, as provided by the so called ‘‘Flatness Theorem’’. Our selection rule uses that(More)
where S is a convex set conveyed by a separation oracle, with no further information (e.g., no bounding ball containing or intersecting S, etc.). Our interest in this problem stems from fundamental issues involving the interplay of (i) the computational complexity of computing a point x ∈ S, (ii) the geometry of S, and (iii) the stability or conditioning of(More)
BACKGROUNDS AND AIMS Functional-structural models are interesting tools to relate environmental and management conditions with forest growth. Their three-dimensional images can reveal important characteristics of wood used for industrial products. Like virtual laboratories, they can be used to evaluate relationships among species, sites and management, and(More)
Condition numbers based on the “distance to ill-posedness” ρ(d) have been shown to play a crucial role in the theoretical complexity of solving convex optimization models. In this paper we present two algorithms and corresponding complexity analysis for computing estimates of ρ(d) for a finite-dimensional convex feasibility problem P (d) in standard primal(More)