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This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…
This paper presents a novel outer approximation algorithm for nonsmooth mixed-integer nonlinear programming (MINLP) problems. The method proceeds by fixing the integer variables and solving the resulting nonlinear convex subproblem. When…
Sparse recovery principles play an important role in solving many nonlinear ill-posed inverse problems. We investigate a variational framework with support Oracle for compressed sensing sparse reconstructions, where the available…
We describe an iterative procedure for optimizing policies, with guaranteed monotonic improvement. By making several approximations to the theoretically-justified procedure, we develop a practical algorithm, called Trust Region Policy…
Deep reinforcement learning has been able to solve various tasks successfully, however, due to the construction of policy gradient and training dynamics, tuning deep reinforcement learning models remains challenging. As one of the most…
Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…
The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…
In recent years, numerous vision and learning tasks have been (re)formulated as nonconvex and nonsmooth programmings(NNPs). Although some algorithms have been proposed for particular problems, designing fast and flexible optimization…
Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…
This paper addresses the problem of Unbalanced Optimal Transport (UOT) in which the marginal conditions are relaxed (using weighted penalties in lieu of equality) and no additional regularization is enforced on the OT plan. In this context,…
In this article, we use the monotonic optimization approach to propose an outcome-space outer approximation by copolyblocks for solving strictly quasiconvex multiobjective programming problems and especially in the case that the objective…
In this article, we derive an iterative scheme through a quasi-Newton technique to capture robust weakly efficient points of uncertain multiobjective optimization problems under the upper set less relation. It is assumed that the set of…
In regularized risk minimization, the associated optimization problem becomes particularly difficult when both the loss and regularizer are nonsmooth. Existing approaches either have slow or unclear convergence properties, are restricted to…
A fundamental challenge in model-based offline reinforcement learning (RL) lies in the trade-off between generalization and robustness against exploitation errors in out-of-distribution (OOD) regions. While OOD samples may capture valid…
We study decision rule approximations for generic multi-stage robust linear optimization problems. We consider linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are…
In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our…
We study the problem of nonepisodic reinforcement learning (RL) for nonlinear dynamical systems, where the system dynamics are unknown and the RL agent has to learn from a single trajectory, i.e., without resets. We propose Nonepisodic…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
This paper discusses an outer-approximation guided optimization method for constrained neural network inverse problems with rectified linear units. The constrained neural network inverse problems refer to an optimization problem to find the…
We consider the maximization problem of monotone submodular functions under an uncertain knapsack constraint. Specifically, the problem is discussed in the situation that the knapsack capacity is not given explicitly and can be accessed…