相关论文: Locally Lipschitz vector optimization problems: se…

We develop a principled approach to obtain exact computer-aided worst-case guarantees on the performance of second-order optimization methods on classes of univariate functions. We first present a generic technique to derive interpolation…

Direct collocation for Bolza optimal control yields discrete Karush-Kuhn-Tucker (KKT) points, while practical solvers expose only discrete quantities such as primal-dual iterates, reduced Hessians, and Jacobians. This creates a gap between…

The paper is devoted to the study of regularized versions of multiobjective optimization problems described by directionally Lipschitzian functions. Such regularizations appear in proximal-type algorithms of multiobjective optimization,…

This is a tutorial and survey paper on Karush-Kuhn-Tucker (KKT) conditions, first-order and second-order numerical optimization, and distributed optimization. After a brief review of history of optimization, we start with some preliminaries…

The real-time solution of parametric optimization problems is critical for applications that demand high accuracy under tight real-time constraints, such as model predictive control. To this end, this work presents a learning-based…

This paper studies a multiobjective bilevel optimization problem where each objective is a fractional function. By reformulating the problem into a single-level one, we establish refined necessary and sufficient optimality conditions. These…

We consider a special class of nonconvex semidefinite programming problems and show that every point satisfying the Karush--Kuhn--Tucker (KKT) conditions is globally optimal despite nonconvexity. This property is related to pseudoconvex…

This paper re-examines a continuous optimization framework dubbed NOTEARS for learning Bayesian networks. We first generalize existing algebraic characterizations of acyclicity to a class of matrix polynomials. Next, focusing on a…

We present an algorithm for learning parametric constraints from locally-optimal demonstrations, where the cost function being optimized is uncertain to the learner. Our method uses the Karush-Kuhn-Tucker (KKT) optimality conditions of the…

In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To this end, we introduce a new notion of localised metric…

In this paper, we analyze optimal control problems governed by semilinear parabolic equations. Box constraints for the controls are imposed and the cost functional involves the state and possibly a sparsity-promoting term, but not a…

We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…

This paper addresses the class of continuous-time nonlinear programming problems with equality and inequality constraints. The paper presents necessary optimality conditions of the sequential form. To be more precise, a sequence of…

The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many…

We establish or refute the optimality of inexact second-order methods for unconstrained nonconvex optimization from the point of view of worst-case evaluation complexity, improving and generalizing the results of Cartis, Gould and Toint…

Recently, a new local optimality concept for minimax problems, termed calm local minimax points, has been introduced. In this paper, we extend this concept to a general class of nonsmooth, nonconvex nonconcave minimax problems with coupled…

We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local regions around points, in either average or maximum sense. The…

This paper explores optimality conditions in optimization problems involving generalized invex fuzzy functions. We extend the classical KKT framework to settings in which the objective and constraint functions are nonsmooth, vector-valued,…

The constant rank constraint qualification, introduced by Janin in 1984 for nonlinear programming, has been extensively used for sensitivity analysis, global convergence of first- and second-order algorithms, and for computing the…

This paper is devoted to the study of approximate solutions for a multiobjective interval-valued optimization problem based on an interval order. We establish new existence theorems of approximate solutions for such a problem under some…