We discuss first and second order optimality conditions for nonlinear second-order cone programming problems, and their relation with semidefinite programming problems. For doing this we extend in an abstract setting the notion of optimal partition. Then we state a characterization of strong regularity in terms of second order optimality conditions.

Analysis in conic programming with applications to optimality and stability.

The paper concerns parameterized equilibria governed by generalized equations whose multivalued parts are modeled via regular normals to nonconvex conic constraints. Our main goal is to derive a precise pointwise second-order formula for calculating the graphical derivative of the solution maps to such generalized equations that involves Lagrange multipliers of the corresponding KKT systems and critical cone directions. Then we apply the obtained formula to characterizing a Lipschitzian stability notion for the solution maps that is known as isolated calmness.Mathematics Subject Classification (2010): primary 49J53, 49J52; secondary 90C31.

We develop a theoretical framework to assess the sustainability of fishery management strategies, when the bioeconomic dynamics are marked by uncertainty and several conflicting objectives have to be accounted for. Stochastic viability ranks management strategies according to their probability to sustain economic and ecological outcomes over time. The approach is extended to build stochastic sustainable production possibility frontiers representing the trade-offs between sustainability objectives at any risk level, given the current state of the fishery. This framework is applied to a Chilean fishery faced with El Nio uncertainty. We study the viability of effort and quota strategies when catch and biomass levels have to be sustained. We show that (1) for these sustainability objectives, whatever the level of the outcomes to be sustained, quota-based management results in a better viability probability than effort-based management, and (2) the fishery's historical quota levels were not sustainable given the stock levels in the early 2000sCNRS Conicyt-Chile INRIA French Ministry of Foreign Affairs Conicyt-Chile, under ACT 10336 FONDECYT 1110888 BASAL Project (Centro de Modelamiento Matematico, Universidad de Chile) project BIONATURE of CIRIC, INRIA-Chil

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