Abstract This paper deals with a robust multiobjective optimization problem involving nonsmooth/nonconvex real-valued functions. Under an appropriate constraint qualification, we establish necessary optimality conditions for weakly efficient solutions of the considered problem. These are presented in terms Karush-Kuhn-Tucker multipliers and convexificators related Examples illustrating our find...

This paper studies several classes of nonconvex optimization problems defined over convex cones, establishing connections between them and demonstrating that they can be equivalently formulated as convex completely positive programs. The problems being studied include: a conic quadratically constrained quadratic program (QCQP), a conic quadratic program with complementarity constraints (QPCC), ...

We present two new constraint qualifications (CQ) that are weaker than the recently introduced Relaxed Constant Positive Linear Dependence (RCPLD) constraint qualification. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set of gradients whose properties had...

This paper studies several classes of nonconvex optimization problems defined over convex cones, establishing connections between them and demonstrating that they can be equivalently formulated as convex completely positive programs. The problems being studied include: a quadratically constrained quadratic program (QCQP), a quadratic program with complementarity constraints (QPCC), and rank con...

Abstract Considering constrained choice, practitioners and theorists frequently invoke a Lagrangian to generate optimality conditions. Regular use of that vehicle requires, however, some constraint qualification . Yet many economists go easy on the mathematics issue. Conversely, few mathematicians elaborate economics context. Thereby both parties leave lacunas as didactics or intuition. This no...

For some optimal control problems with pathwise state constraints the standard versions of the necessary conditions of optimality are unable to provide useful information to select minimizers. There exist some literature on stronger forms of the maximum principle, the so-called nondegenerate necessary conditions, that can be informative for those problems. These conditions can be applied when c...

This paper discusses an implicit reformulation of the MPEC (mathematical program with complementarity constraints) problem in order to solve a robust structural optimization with a non-probabilistic uncertainty model of the static load. We first show the relation among the robust constraint satisfaction, worst scenario detection, and robust structural optimization, and derive the MPEC formulati...

A convex semidefinite programming problem is a convex constrained optimization problem, where the constraints are linear matrix inequalities, for which the standard Lagrangian condition is sufficient for optimality. However, this condition requires constraint qualifications to completely characterize optimality. We present a necessary and sufficient condition for optimality without a constraint...

We develop a new notion of second-order complementarity with respect to the tangent subspace associated to second-order necessary optimality conditions by the introduction of so-called tangent multipliers. We prove that around a local minimizer, a second-order stationarity residual can be driven to zero while controlling the growth of Lagrange multipliers and tangent multipliers, which gives a ...