It is known that the condition $mathfrak {Re} left{zf'(z)/f(z)right}>0$, $|z|

We analyze the optimal value function v associated with a general parametric optimization problem via theory of viscosity solutions. The novelty is that we obtain regularity properties by showing it solution to set first-order equations. As consequence, in Banach spaces, provide sufficient conditions for local and global Lipschitz v. also derive, finite dimensions, optimality through comparison...

Abstract. A nonlinearly constrained optimization problem can be solved by the exact penalty approach involving nondifferentiable functions and max 0 . In [11], a trust region affine scaling approach based on a 2-norm subproblem is proposed for solving a nonlinear 1 problem. The (quadratic) approximation and the trust region subproblem are defined using affine scaling techniques. Explicit suffic...

We develop an affine-scaling algorithm for box-constrained optimization which has the property that each iterate is a scaled cyclic Barzilai–Borwein (CBB) gradient iterate that lies in the interior of the feasible set. Global convergence is established for a nonmonotone line search, while there is local R-linear convergence at a nondegenerate local minimizer where the second-order sufficient op...

Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem impossible to solve by the classical method of spike variation. In this paper, we introduce a new approach to solve this open problem and we establish necessary ...

We study the Celis-Dennis-Tapia (CDT) problem: minimize a non-convex quadratic function over the intersection of two ellipsoids. In contrast to the well-studied trust region problem where the feasible set is just one ellipsoid, the CDT problem is not yet fully understood. Our main objective in this paper is to narrow the difficulty gap that occurs when the Hessian of the Lagrangian is indefinit...

This paper is devoted to the analysis and numerical solution of distributed optimal control of the Navier-Stokes equations in presence of bilateral pointwise control constraints. The analysis of the problem involves the proof of existence of an optimal solution, as well as the presentation of necessary and sufficient conditions for optimality. For the numerical solution of the problem we apply ...

We consider a stochastic control problem of nonlinear forward-backward systems, where the set of strict (classical) controls need not be convex and the coefficients depend explicitly on the variable control. By introducing a new approach, we establish necessary as well as sufficient conditions of optimality, in the form of global stochastic maximum principle, for two models. The first concerns ...