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We consider convex optimization problems with prioritized equality constraints, which may be infeasible. In many applications, such as network optimization and image reconstruction, it is often desirable to compute solutions that satisfy…
This paper addresses an open problem in the area of linear quadratic optimal control. We consider the regular, infinite-horizon, stability-modulo-a-subspace, indefinite linear quadratic problem under the assumption that the dynamics are…
In this paper, we undertake an investigation into the utility maximization problem faced by an economic agent who possesses the option to switch jobs, within a scenario featuring the presence of a mandatory retirement date. The agent needs…
In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This interest surge is due to advancements in computing…
In this note, we prove that minimizers of convex functionals with a convexity constraint and a general class of Lagrangians can be approximated by solutions to fourth-order equations of Abreu type. Our result generalizes that of Le (Twisted…
We introduce a new form of Lagrangian and propose a simple first-order algorithm for nonconvex optimization with nonlinear equality constraints. We show the algorithm generates bounded dual iterates, and establish the convergence to KKT…
In the paper we consider the infinite horizon control problems on the interval with free right-hand endpoint. We obtain the necessary conditions of strict optimality. The method of the proof actually follows the classic paper by Halkin, and…
In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
In this paper, we establish an exponential periodic turnpike property for linear quadratic optimal control problems governed by periodic systems in infinite dimension. We show that the optimal trajectory converges exponentially to a…
The Yakubovich Frequency Theorem, in its periodic version and in its general nonautonomous extension, establishes conditions which are equivalent to the global solvability of a minimization problem of infinite horizon type, given by the…
This paper proposes and analyzes a proximal augmented Lagrangian (NL-IAPIAL) method for solving smooth nonconvex composite optimization problems with nonlinear $\cal K$-convex constraints, i.e., the constraints are convex with respect to…
An accurate approximation of solutions to elliptic problems in infinite domains is challenging from a computational point of view. This is due to the need to replace the infinite domain with a sufficiently large and bounded computational…
We propose an algorithm for general nonlinear conic programming which does not require the knowledge of the full cone, but rather a simpler, more tractable, approximation of it. We prove that the algorithm satisfies a strong global…
Decision processes with incomplete state feedback have been traditionally modeled as Partially Observable Markov Decision Processes. In this paper, we present an alternative formulation based on probabilistic regular languages. The proposed…
We prove a maximum principle for the problem of optimal control for a fractional diffusion with infinite horizon. Further, we show existence of fractional backward stochastic differential equations on infinite horizon. We illustrate our…
In this paper, we investigate an interesting and important stopping problem mixed with stochastic controls and a \textit{nonsmooth} utility over a finite time horizon. The paper aims to develop new methodologies, which are significantly…
In this paper we study a utility maximization problem with random horizon and reduce it to the analysis of a specific BSDE, which we call BSDE with singular coefficients, when the support of the default time is assumed to be bounded. We…
We consider the problem of planning with participation constraints introduced in [Zhang et al., 2022]. In this problem, a principal chooses actions in a Markov decision process, resulting in separate utilities for the principal and the…
In this paper, we study the necessary and sufficient conditions for ensuring the well-posedness of the stochastic singular systems. Moreover, we investigate the stochastic singular linear-quadratic control problems, considering both finite…