Related papers: Relaxations for Non-Separable Cardinality/Rank Pen…
This paper considers a quadratically-constrained cardinality minimization problem with applications to digital filter design, subset selection for linear regression, and portfolio selection. Two relaxations are investigated: the continuous…
This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints…
In sparse optimization, the $\ell_{1}$ norm is widely adopted for its convexity, yet it often yields solutions with smaller magnitudes than expected. To mitigate this drawback, various non-convex sparse penalties have been proposed. Some…
This paper studies high-order evaluation complexity for partially separable convexly-constrained optimization involving non-Lipschitzian group sparsity terms in a nonconvex objective function. We propose a partially separable adaptive…
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…
We give a novel formal theoretical framework for unsupervised learning with two distinctive characteristics. First, it does not assume any generative model and based on a worst-case performance metric. Second, it is comparative, namely…
Low-rank regularization (LRR) has been widely applied in various machine learning tasks, but the associated optimization is challenging. Directly optimizing the rank function under constraints is NP-hard in general. To overcome this…
This paper is concerned with the calmness of a partial perturbation to the composite rank constraint system, an intersection of the rank constraint set and a general closed set, which is shown to be equivalent to a local Lipschitz-type…
In this two-part study we develop a unified approach to the analysis of the global exactness of various penalty and augmented Lagrangian functions for finite-dimensional constrained optimization problems. This approach allows one to verify…
Under the linear regression framework, we study the variable selection problem when the underlying model is assumed to have a small number of nonzero coefficients (i.e., the underlying linear model is sparse). Non-convex penalties in…
We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…
We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…
We consider nonconvex constrained optimization problems and propose a new approach to the convergence analysis based on penalty functions. We make use of classical penalty functions in an unconventional way, in that penalty functions only…
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate…
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate…
This paper defines a strong convertible nonconvex(SCN) function for solving the unconstrained optimization problems with the nonconvex or nonsmooth(nondifferentiable) function. First, many examples of SCN function are given, where the SCN…
We propose a totally corrective boosting algorithm with explicit cardinality regularization. The resulting combinatorial optimization problems are not known to be efficiently solvable with existing classical methods, but emerging quantum…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The…
We investigate convexification for convex quadratic optimization with step function penalties. Such problems can be cast as mixed-integer quadratic optimization problems, where binary variables are used to encode the non-convex step…