Related papers: Second-Order Strong Optimality and Second-Order Du…
Much is known about when a locally optimal solution depends in a single-valued Lipschitz continuous way on the problem's parameters, including tilt perturbations. Much less is known, however, about when that solution and a uniquely…
We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They…
In this paper, we study a nonsmooth/nonconvex multiobjective optimization problem with uncertain constraints in arbitrary Asplund spaces. We first provide necessary optimality condition in a fuzzy form for approximate weakly robust…
This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex…
This paper investigates a specific class of nonsmooth nonconvex optimization problems in the face of data uncertainty, namely, robust optimization problems, where the given objective function can be expressed as a difference of two…
This paper extends the SQP-approach of the well-known bundle-Newton method for nonsmooth unconstrained minimization to the nonlinearly constrained case. Instead of using a penalty function or a filter or an improvement function to deal with…
This work is concerned with second-order necessary and sufficient optimality conditions for optimal control of a non-smooth semilinear elliptic partial differential equation, where the nonlinearity is the non-smooth max-function and thus…
Weak sharp minimality is a notion emerged in optimization, whose utility is largeley recognized in the convergence analysis of algorithms for solving extremum problems as well as in the study of the perturbation behaviour of such problems.…
This paper explores local second-order weak sharp minima for a broad class of nonconvex optimization problems. We propose novel second-order optimality conditions formulated through the use of classical and lower generalized support…
Additive manufacturing by laser fusion on a metal oxides powder bed has developed considerably in the last few years and allows to produce a wide range of complex parts. The mathematical models correspond to initial boundary value problems…
One of the most important optimality conditions to aid to solve a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality…
This paper is concerned with second-order optimality conditions for the mathematical program with semidefinite cone complementarity constraints (SDCMPCC).To achieve this goal, we first provide an exact characterization on the second-order…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
Most numerical methods developed for solving nonlinear programming problems are designed to find points that satisfy certain optimality conditions. While the Karush-Kuhn-Tucker conditions are well-known, they become invalid when constraint…
We address second-order optimality conditions for optimal control problems involving sparsity functionals which induce spatio-temporal sparsity patterns. We employ the notion of (weak) second subderivatives. With this approach, we are able…
Over the last years, minimization problems over spaces of measures have received increased interest due to their relevance in the context of inverse problems, optimal control and machine learning. A fundamental role in their numerical…
This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…
We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no…
This paper addresses the study of a new class of nonsmooth optimization problems, where the objective is represented as a difference of two generally nonconvex functions. We propose and develop a novel Newton-type algorithm to solving such…
The alternating direction method of multipliers (ADMM) is widely used for solving large-scale semidefinite programs (SDPs), yet on instances with multiple primal-dual optimal solution pairs, it often enters prolonged slow-convergence…