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Bio-inspired algorithms such as neural network algorithms and genetic algorithms have received a significant amount of attention in both academic and engineering societies. In this paper, based on the observation of two major survival rules…
In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…
This paper considers the problem of minimizing an expectation function over a closed convex set, coupled with a {\color{black} functional or expectation} constraint on either decision variables or problem parameters. We first present a new…
The particle swarm optimization (PSO) algorithm has been recently introduced in the non--linear programming, becoming widely studied and used in a variety of applications. Starting from its original formulation, many variants for…
Particle swam optimization (PSO) is a popular stochastic optimization method that has found wide applications in diverse fields. However, PSO suffers from high computational complexity and slow convergence speed. High computational…
A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving…
Traditional methods present a very restrictive range of applications, mainly limited by the features of the function to be optimized and of the constraint functions. In contrast, evolutionary algorithms present almost no restriction to the…
We consider stochastic optimization problems with non-convex functional constraints, such as those arising in trajectory generation, sparse approximation, and robust classification. To this end, we put forth a recursive momentum-based…
Population-based methods can cope with a variety of different problems, including problems of remarkably higher complexity than those traditional methods can handle. The main procedure consists of successively updating a population of…
We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior…
We study PCA as a stochastic optimization problem and propose a novel stochastic approximation algorithm which we refer to as "Matrix Stochastic Gradient" (MSG), as well as a practical variant, Capped MSG. We study the method both…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
The partially observable constrained optimization problems (POCOPs) impede data-driven optimization techniques since an infeasible solution of POCOPs can provide little information about the objective as well as the constraints. We endeavor…
Particle swarm optimization (PSO) is an iterative search method that moves a set of candidate solution around a search-space towards the best known global and local solutions with randomized step lengths. PSO frequently accelerates…
This paper proposes a novel population-based meta-heuristic optimization algorithm, called Perfectionism Search Algorithm (PSA), which is based on the psychological aspects of perfectionism. The PSA algorithm takes inspiration from one of…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized…
We developed a corporative stochastic approximation (CSA) type algorithm for semi-infinite programming (SIP), where the cut generation problem is solved inexactly. First, we provide general error bounds for inexact CSA. Then, we propose two…
There is an increasing need in solving high-dimensional optimization problems under non-deterministic environment. The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for…
The global optimization of a high-dimensional black-box function under black-box constraints is a pervasive task in machine learning, control, and engineering. These problems are challenging since the feasible set is typically non-convex…