相关论文: Trust-Region Method for Optimization of Set-Valued…

Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…

We propose a novel framework for analyzing convergence rates of stochastic optimization algorithms with adaptive step sizes. This framework is based on analyzing properties of an underlying generic stochastic process, in particular by…

In this article, we consider the residual regularization path-following method with the trust-region updating strategy for the linear complementarity problem. This time-stepping selection based on the trust-region updating strategy…

Consider the problem of finding an optimal value of some objective functional subject to constraints over numerical domain. This type of problem arises frequently in practical engineering tasks. Nowdays almost all general methods for…

This paper proposes a random subspace trust-region algorithm for general convex-constrained derivative-free optimization (DFO) problems. Similar to previous random subspace DFO methods, the convergence of our algorithm requires a certain…

We investigate the problem of parameter selection for the scaled trust-region Newton (STRN) algorithm in solving bound-constrained nonlinear equations. Numerical experiments were performed on a large number of test problems to find the best…

We propose, analyze, and test a proximal-gradient method for solving regularized optimization problems with general constraints. The method employs a decomposition strategy to compute trial steps and uses a merit function to determine step…

Stein variational inference (SVI) is a sample-based approximate Bayesian inference technique that generates a sample set by jointly optimizing the samples' locations to minimize an information-theoretic measure of discrepancy with the…

Machine learning (ML) problems are often posed as highly nonlinear and nonconvex unconstrained optimization problems. Methods for solving ML problems based on stochastic gradient descent are easily scaled for very large problems but may…

We propose a new globalization strategy that can be used in unconstrained optimization algorithms to support rapid convergence from remote starting points. Our approach is based on using multiple points at each iteration to build a…

Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…

We establish a broad methodological foundation for mixed-integer optimization with learned constraints. We propose an end-to-end pipeline for data-driven decision making in which constraints and objectives are directly learned from data…

Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…

Lens designers routinely use optimization in their everyday practice. Local optimization algorithms lead to the nearest minimum. In this paper, a new deterministic approach for multi-extremum optimization is proposed. Optimal solutions for…

In this paper, we consider the nonsmooth convex optimization problems over the fixed point constraint sets of firmly nonexpansive operators. To find an optimal solution of the problem, we present an iterative method based on the hybrid…

Value iteration is a popular algorithm for finding near optimal policies for POMDPs. It is inefficient due to the need to account for the entire belief space, which necessitates the solution of large numbers of linear programs. In this…

A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…

Two-phase methods are commonly used to solve bi-objective combinatorial optimization problems. In the first phase, all extreme supported nondominated points are generated through a dichotomic search. This phase also allows the…

Adaptive regularized framework using cubics has emerged as an alternative to line-search and trust-region algorithms for smooth nonconvex optimization, with an optimal complexity amongst second-order methods. In this paper, we propose and…

In the present paper, some aspects of the finite-dimensional theory of set-inclusive generalized equations are studied. Set-inclusive generalized equations are problems arising in several contexts of optimization and variational analysis,…