In this paper we consider a mathematical program with second-order cone complementarity constraints (SOCMPCC). The SOCMPCC generalizes the mathematical program with complementarity constraints (MPCC) in replacing the set of nonnegative reals by a second-order cone. We show that if the SOCMPCC is considered as an optimization problem with convex cone constraints, then Robinson’s constraint quali...

In this paper we present a robust duality theory for generalized convex programming problems in the face of data uncertainty within the framework of robust optimization. We establish robust strong duality for an uncertain nonlinear programming primal problem and its uncertain Lagrangian dual by showing strong duality between the deterministic counterparts: robust counterpart of the primal model...

The normal cone to a constraint set plays a key role in optimization theory, algorithms, and applications. We consider the question of how to approximate the normal cone to a set under the assumption that the set is provided through an oracle function or collection of oracle functions, but contains some exploitable structure. We provide a new simplex gradient based approximation technique that ...

This paper discusses an implicit reformulation of a class of MPEC (mathematical program with equilibrium constraints) problems. We particularly focus on an MPEC problem arising from the robust optimization of elastic structures subjected to the uncertain external load. We first review the relation between the worst-case detection and robust constraint satisfaction of the structural responses, a...

In this paper we study the bilevel dynamic problem, which is a hierarchy of two dynamic optimization problems, where the constraint region of the upper level problem is determined implicitly by the solutions to the lower level optimal control problem. To obtain optimality conditions, we reformulate the bilevel dynamic problem as a single level optimal control problem that involves the value fun...

We develop a new notion of second-order complementarity with respect to the tangent subspace related 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 new...

In this paper, Karush-Kuhn-Tucker type robust necessary optimality conditions for a nonsmooth interval-valued optimization problem (UCIVOP) are formulated using the concept of LU-optimal solution and generalized Slater constraint qualification (GRSCQ). These shown to be sufficient under convexity. The Wolfe Mond-Weir dual problems over cones convexity assumptions, usual duality results establis...

The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar’s constraint qualification holds. In this paper, we prove the maximal monotonicity of A + ∂f provided that A is a maximally monotone linear relation, and f is a proper lower semicontinuous convex function satisfying domA ∩ int dom...

Several fundamental concepts such as the basic constraint qualification (BCQ), the strong conical hull intersection property (CHIP), and the perturbations for convex systems of inequalities in Banach spaces (over R or C) are extended and studied; here the systems are not necessarily finite. Their relationships with each other in connection with the best approximations are investigated. As appli...

We deal with an optimal control problem of the Bolza type, where the controlled system is governed by a generalized sweeping process, which is a special differential inclusion with discontinuous right-hand side. Employing a suitable constraint qualification, we restate the problem using distance functions and use the fuzzy sum rule to obtain fuzzy optimality conditions. Furthermore, we derive p...