Related papers: New sharp necessary optimality conditions for math…
We study a class of quadratically constrained quadratic programs (QCQPs), called {\em diagonal QCQPs\/}, which contain no off-diagonal terms $x_j x_k$ for $j \ne k$, and we provide a sufficient condition on the problem data guaranteeing…
Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of…
This paper explores local second-order weak sharp minima for a broad class of nonconvex optimization problems. We propose novel second-order optimality conditions formulated through the use of classical and lower generalized support…
Chance-constrained programs (CCP) represent a trade-off between conservatism and robustness in optimization. In many CCPs, one optimizes an objective under a probabilistic constraint continuously parameterized by a random vector $\xi$. In…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
Many practical applications of control require that constraints on the inputs and states of the system be respected, while optimizing some performance criterion. In the presence of model uncertainties or disturbances, for many control…
We consider the task of training machine learning models with data-dependent constraints. Such constraints often arise as empirical versions of expected value constraints that enforce fairness or stability goals. We reformulate…
The Principle of Maximum Conformality (PMC) provides scale-fixed perturbative QCD predictions which are independent of the choice of the renormalization scheme, as well as the choice of the initial renormalization scale. In this article, we…
We consider a class of optimization problems defined by a system of linear equations with min and max operators. This class of optimization problems has been studied under restrictive conditions, such as, (C1) the halting or stability…
In this paper, we propose some new semidefinite relaxations for a class of nonconvex complex quadratic programming problems, which widely appear in the areas of signal processing and power system. By deriving new valid constraints to the…
In a common formulation of semi-infinite programs, the infinite constraint set is a requirement that a function parametrized by the decision variables is nonnegative over an interval. If this function is sufficiently closely approximable by…
In this paper we consider a sufficiently broad class of nonlinear mathematical programs with disjunctive constraints, which, e.g., include mathematical programs with complemetarity/vanishing constraints. We present an extension of the…
This paper introduces a new modeling framework for optimization under uncertainty, called Probable Event Constrained Optimization (PECO). Unlike conventional chance-constrained formulations, which only limit the probability of constraint…
We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reasonable notions of linear-type monotonicity of fixed point…
The nonsmooth composite matrix optimization problem (CMatOP), in particular, the matrix norm minimization problem, is a generalization of the matrix conic programming problem with wide applications in numerical linear algebra, computational…
Contraction-Based Nonlinear Model Predictive Control (NMPC) formulations are attractive because of the generally short prediction horizons they require and the needless use of terminal set computation that are commonly necessary to…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
Motivated by applications, we consider here new operator theoretic approaches to Conditional mean embeddings (CME). Our present results combine a spectral analysis-based optimization scheme with the use of kernels, stochastic processes, and…
Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…
Bilevel hyperparameter optimization has received growing attention thanks to the fast development of machine learning. Due to the tremendous size of data sets, the scale of bilevel hyperparameter optimization problem could be extremely…