Related papers: A convex penalty for switching control of partial …
This paper deals with optimal control problems described by a controlled version of Moreau's sweeping process governed by convex polyhedra, where measurable control actions enter additive perturbations. This class of problems, which…
We consider an optimal shape design problem for the plate equation, where the variable thickness of the plate is the design function. This problem can be formulated as a control in the coefficient PDE-constrained optimal control problem…
Given an infeasible, unbounded, or pathological convex optimization problem, a natural question to ask is: what is the smallest change we can make to the problem's parameters such that the problem becomes solvable? In this paper, we address…
We suggest an adaptive version of a partial linearization method for composite optimization problems. The goal function is the sum of a smooth function and a non necessary smooth convex separable function, whereas the feasible set is the…
We propose a decentralized penalty method for general convex constrained multi-agent optimization problems. Each auxiliary penalized problem is solved approximately with a special parallel descent splitting method. The method can be…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…
In this paper, we consider a mixed boundary value problem with a double phase partial differential operator, an obstacle effect and a multivalued reaction convection term. Under very general assumptions, an existence theorem for the mixed…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
We consider a general decomposable convex optimization problem. By using right-hand side allocation technique, it can be transformed into a collection of small dimensional optimization problems. The master problem is a convex non-smooth…
This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…
In this paper, we consider the problem of multi-objective optimal control of a dynamical system with additive and multiplicative noises with given second moments and arbitrary probability distributions. The objectives are given by quadratic…
In this paper, we study a variant of the quadratic penalty method for linearly constrained convex problems, which has already been widely used but actually lacks theoretical justification. Namely, the penalty parameter steadily increases…
We consider an extension of a noncooperative game problem where players have joint binding constraints. In this case, justification of a generalized equilibrium point needs a reasonable mechanism for attaining this state. We suggest to…
We propose an approximation scheme for a class of semilinear parabolic equations that are convex and coercive in their gradients. Such equations arise often in pricing and portfolio management in incomplete markets and, more broadly, are…
We prove a stochastic maximum principle ofPontryagin's type for the optimal control of a stochastic partial differential equationdriven by white noise in the case when the set of control actions is convex. Particular attention is paid to…
Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…
In many problems in optimal control, one seeks to minimise an objective function subject to constraints on the velocity of the system. Imposing these constraints directly -- the ``hard-constrained'' approach -- is often analytically and…
A general class of nonconvex optimization problems is considered, where the penalty is the composition of a linear operator with a nonsmooth nonconvex mapping, which is concave on the positive real line. The necessary optimality condition…
We develop two penalty based difference of convex (DC) algorithms for solving chance constrained programs. First, leveraging a rank-based DC decomposition of the chance constraint, we propose a proximal penalty based DC algorithm in the…
We consider a general optimization problem of minimizing a composite objective functional defined over a class of probability distributions. The objective is composed of two functionals: one is assumed to possess the variational…