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Minimax optimization problems are an important class of optimization problems arising from both modern machine learning and from traditional research areas. We focus on the stability of constrained minimax optimization problems based on the…
The paper suggests a new --- to the best of the author's knowledge --- characterization of decisions which are optimal in the multi-objective optimization problem with respect to a definite proper preference cone, a Euclidean cone with a…
In the current work, we have formulated the optimal bit-allocation problem for a scalable codec of images or videos as a constrained vector-valued optimization problem and demonstrated that there can be many optimal solutions, called Pareto…
We establish a new extremal inequality, which is further leveraged to give a complete characterization of the rate region of the vector Gaussian CEO problem with the trace distortion constraint. The proof of this extremal inequality hinges…
In this paper, we establish the existence of the efficient solutions for polynomial vector optimization problems on a nonempty closed constraint set without any convexity and compactness assumptions. We first introduce the relative…
We provide necessary and sufficient conditions for robust efficiency (in the sense of Ehrgott et al. (2014)) to multiobjective optimization problems that depend on uncertain parameters. These conditions state that a solution is robust…
It is proved that, for an indefinite quadratic programming problem under linear constraints, any iterative sequence generated by the Proximal DC decomposition algorithm $R$-linearly converges to a Karush-Kuhn-Tucker point, provided that the…
The NP-hard problem of optimizing a quadratic form over the unimodular vector set arises in radar code design scenarios as well as other active sensing and communication applications. To tackle this problem (which we call unimodular…
Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…
The asymptotic Karush-Kuhn-Tucker (AKKT) optimality conditions are distinguished from other approaches in the literature by virtue of their capacity to be effectively derived through numerical methods, such as the utilization of an…
We suggest a novel approach for the efficient and reliable approximation of the Pareto front of sufficiently smooth unconstrained bi-criteria optimization problems. Optimality conditions formulated for weighted sum scalarizations of the…
This paper is concerned with a class of stochastic optimization problems defined on a Banach space with almost sure conic-type constraints. For this class of problems, we investigate the consistency of optimal values and solutions…
Computing approximate Karush--Kuhn--Tucker (KKT) points for constrained nonconvex programs is a fundamental problem in mathematical programming. Interior-point trust-region (IPTR) methods are particularly attractive for such problems…
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…
We develop refined Karush-Kuhn-Tucker (KKT) and Fritz-John (FJ)-type optimality conditions for nonsmooth, nonconvex mathematical pro\-gra\-mming problems. We pay special attention in the case that the functional constraint belongs to a…
In the first part of this work [32], we introduce a convex parabolic relaxation for quadratically-constrained quadratic programs, along with a sequential penalized parabolic relaxation algorithm to recover near-optimal feasible solutions.…
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…
We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They…
In this article we study an optimal control problem subject to the Fokker-Planck equation \[ \partial_t \rho - \nu \Delta \rho - {\rm div } \big(\rho B[u]\big) = 0. \] The control variable $u$ is time-dependent and possibly…
We investigate the relationship between algorithmic fractal dimensions and the classical local fractal dimensions of outer measures in Euclidean spaces. We introduce global and local optimality conditions for lower semicomputable outer…