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This paper presents a practical method for finding the globally optimal solution to the sum-of-ratios problem arising in image processing, engineering and management. Unlike traditional methods which may get trapped in local minima due to…
Bilevel optimization has been successfully applied to many important machine learning problems. Algorithms for solving bilevel optimization have been studied under various settings. In this paper, we study the nonconvex-strongly-convex…
Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…
Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
We study nonconvex distributed optimization in multi-agent networks with time-varying (nonsymmetric) connectivity. We introduce the first algorithmic framework for the distributed minimization of the sum of a smooth (possibly nonconvex and…
When considering an unconstrained minimization problem, a standard approach is to solve the optimality system with a Newton method possibly preconditioned by, e.g., nonlinear elimination. In this contribution, we argue that nonlinear…
We present an optimization-based approach to stochastic control problems with nonclassical information structures. We cast these problems equivalently as optimization prob- lems on joint distributions. The resulting problems are necessarily…
There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…
Optimization problems are considered in the framework of tropical algebra to minimize and maximize a nonlinear objective function defined on vectors over an idempotent semifield, and calculated using multiplicative conjugate transposition.…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
In this paper, we investigate the nonemptiness of weak Pareto efficient solution set for a class of nonsmooth vector optimization problems on a nonempty closed constraint set without any boundedness and convexity assumptions. First, we…
We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex…
Tree convex sets refer to a collection of sets such that each set in the collection is a subtree of a tree whose nodes are the elements of these sets. They extend the concept of row convex sets each of which is an interval over a total…
In connection with the needs of solving optimization problems, the development of conditional minimization methods with convenient numerical implementation continues to attract the attention of mathematicians. In this monograph we propose…