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Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…
We examine the duality theory for a class of non-convex functions obtained by composing a convex function with a continuous one. Using Fenchel duality, we derive a dual problem that satisfies weak duality under general assumptions. To…
We consider optimal control problems governed by systems describing the flow of an incompressible second grade fluid with Dirichlet boundary conditions. We prove the existence of an optimal solution, derive the corresponding necessary…
We employ a fuzzy optimality condition for the Frechet subdifferential and some advanced techniques of variational analysis such as formulae for the subdifferentials of an infinite family of nonsmooth functions and the coderivative…
The aim of this work is to study, from an intrinsic and geometric point of view, second-order constrained variational problems on Lie algebroids, that is, optimization problems defined by a cost functional which depends on higher-order…
In this paper, we present some second-order sufficient conditions in terms of the Demyanov-Pevnyi's second-order directional derivatives for efficiency of $C^1$ vector optimization problems with constraints. Our results improve and…
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…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
Negative Curvature and Second-order optimality for regularized SQP
In this paper, we propose a new control design scheme for solving the obstacle avoidance problem for nonlinear driftless control-affine systems. The class of systems under consideration satisfies controllability conditions with iterated Lie…
We consider fractional order optimal control problems in which the dynamic control system involves integer and fractional order derivatives and the terminal time is free. Necessary conditions for a state/control/terminal-time triplet to be…
This paper studies a multiobjective bilevel optimization problem where each objective is a fractional function. By reformulating the problem into a single-level one, we establish refined necessary and sufficient optimality conditions. These…
We introduce and study a new dual condition which characterizes zero duality gap in nonsmooth convex optimization. We prove that our condition is weaker than all existing constraint qualifications, including the closed epigraph condition.…
We study the theoretical convergence properties of random-search methods when optimizing non-convex objective functions without having access to derivatives. We prove that standard random-search methods that do not rely on second-order…
We prove higher-order Euler-Lagrange and DuBois-Reymond stationary conditions to fractional action-like variational problems. More general fractional action-like optimal control problems are also considered.
In this article we study optimal control problems for systems that are affine in one part of the control variable. Finitely many equality and inequality constraints on the initial and final values of the state are considered. We investigate…
This paper studies multiobjective optimal control problems in the continuous-time framework when the space of states and the space of controls are infinite-dimensional and with lighter smoothness assumptions than the usual ones. The paper…
A second-order regularity theory is developed for solutions to a class of quasilinear elliptic equations in divergence form, including the $p$-Laplace equation, with merely square-integrable right-hand side. Our results amount to the…
In this paper we study an optimal control problem with nonsmooth mixed state and control constraints. In most of the existing results, the necessary optimality condition for optimal control problems with mixed state and control constraints…
Whereas in a coordinate-dependent setting the Euler-Lagrange equations establish necessary conditions for solving variational problems in which both the integrands of functionals and the resulting paths are assumed to be sufficiently…