相关论文: New global optimality conditions for nonsmooth DC …
The problem of finding global minima of nonlinear discrete functions arises in many fields of practical matters. In recent years, methods based on discrete filled functions become popular as ways of solving these sort of problems. However,…
Nonconvex optimization problems arise in many areas of computational science and engineering and are (approximately) solved by a variety of algorithms. Existing algorithms usually only have local convergence or subsequence convergence of…
Cardinality constraints in optimization are commonly of $L^0$-type, and they lead to sparsely supported optimizers. An efficient way of dealing with these constraints algorithmically, when the objective functional is convex, is…
This paper addresses the study of a new class of nonsmooth optimization problems, where the objective is represented as a difference of two generally nonconvex functions. We propose and develop a novel Newton-type algorithm to solving such…
Codifferentials and coexhausters are used to describe nonhomogeneous approximations of a nonsmooth function. Despite the fact that coexhausters are modern generalizations of codifferentials, the theories of these two concepts continue to…
We consider stochastic optimization problems involving an expected value of a nonlinear function of a base random vector and a conditional expectation of another function depending on the base random vector, a dependent random vector, and…
Whereas in a coordinate-dependent setting the Euler-Lagrange equations establish necessary conditions for solving variational problems in which both the integrands of functionals and the resulting paths are assumed to be sufficiently…
The difference-of-convex algorithm (DCA) is a well-established nonlinear programming technique that solves successive convex optimization problems. These sub-problems are obtained from the difference-of-convex~(DC) decompositions of the…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
The difference-of-convex (DC) program is an important model in nonconvex optimization due to its structure, which encompasses a wide range of practical applications. In this paper, we aim to tackle a generalized class of DC programs, where…
Conditional gradient methods have attracted much attention in both machine learning and optimization communities recently. These simple methods can guarantee the generation of sparse solutions. In addition, without the computation of full…
In this paper, we consider a class of nonconvex (not necessarily differentiable) optimization problems called generalized DC (Difference-of-Convex functions) programming, which is minimizing the sum of two separable DC parts and one…
Non-convex optimization problems have multiple local optimal solutions. Non-convex optimization problems are commonly found in numerous applications. One of the methods recently proposed to efficiently explore multiple local optimal…
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…
The paper introduces several new concepts for solving nonconvex or nonsmooth optimization problems, including convertible nonconvex function, exact convertible nonconvex function and differentiable convertible nonconvex function. It is…
In this paper, we study a family of non-convex and possibly non-smooth inf-projection minimization problems, where the target objective function is equal to minimization of a joint function over another variable. This problem include…
This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…
In this paper we consider a class of structured nonsmooth difference-of-convex (DC) constrained DC program in which the first convex component of the objective and constraints is the sum of a smooth and nonsmooth functions while their…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
We consider an optimal control problem for an abstract nonlinear dissipative evolution equation. The differential constraint is penalized by augmenting the target functional by a nonnegative global-in-time functional which is null-minimized…