Directory

Augmented reality disability encompasses a range of impairments affecting an individual’s cognitive, sensory, or motor functions, impacting their ability to effectively navigate and interact with augmented reality environments. These disabilities can manifest as difficulties in perceiving visual or auditory stimuli, comprehending instructions, or controlling physical movements in response to augmented reality inputs. By understanding and…

An augmented reality table is a specially equipped table that uses projection technology to overlay digital information onto the table’s surface, creating an interactive and immersive experience. It typically consists of a high-resolution projector, cameras, sensors, and software. This technology allows users to interact with digital content, manipulate virtual objects, and collaborate with others in…

Optimal control dynamic programming (OCDP) is a technique used to solve optimal control problems, which involve finding the best control strategy to achieve a desired objective while satisfying constraints. OCDP is based on Bellman’s equation, which states that the value of an optimal control problem can be calculated as the sum of the current value…

Optimal control in continuous linear systems aims to find control inputs that minimize a cost function while satisfying system dynamics. These systems involve state variables describing the system’s current state and control variables influencing its evolution. Optimal control techniques, such as dynamic programming and Pontryagin’s minimum principle, are used to derive optimal control actions. The…

Applied nonlinear programming leverages mathematical foundations, optimization techniques, and practical applications to solve nonlinear optimization problems encountered in engineering and science. It utilizes gradients and Hessians to determine the direction and curvature of the objective function, and convexity analysis aids in identifying optimal solutions. Optimization algorithms such as gradient descent and Newton’s method are employed…

Optimal control theory is a branch of control theory that provides mathematical methods to determine the optimal trajectory of a dynamic system. It uses mathematical concepts like calculus of variations, differential equations, and Pontryagin’s Maximum Principle to find the optimal control inputs that minimize a given cost function while meeting system constraints. Optimal control has…

Selective optimization and compensation (SOC) is a practice in the financial industry where firms reward employees for generating revenue or minimizing risk, even when doing so conflicts with the interests of clients or the firm itself. SOC can lead to excessive risk-taking, misallocation of capital, and other harmful outcomes. Regulators have sought to address SOC…

Linear programming employs mathematical foundations from linear algebra and convex optimization to approximate solutions for complex problems. It utilizes algorithms like the simplex method to solve models that optimize linear functions subject to linear constraints. Practical applications include resource allocation and scheduling, while computational considerations address complexity issues. Linear programming relates to other optimization techniques,…

The Siam Journal on Optimization, a prominent publication in the optimization field, showcases cutting-edge research in continuous optimization, discrete optimization, and their applications in diverse domains. It features articles covering topics such as derivative-free and nonlinear optimization, combinatorial optimization, stochastic optimization, and optimization for machine learning. The journal’s rigorous peer-review process ensures the dissemination of…

Selective optimization with compensation (SOC) is a theory in Cognitive Science that proposes that people allocate their attention to the most important aspects of a task while compensating for limitations in other areas. This allows individuals to optimize their performance on the task as a whole. Research in Behavioral Economics has shown that SOC can…

Sequential quadratic programming (SQP) is an optimization algorithm used to solve nonlinear constrained optimization problems. It combines the principles of quadratic programming and sequential unconstrained minimization. SQP iteratively solves a sequence of quadratic subproblems that approximate the original problem. Each subproblem is defined by a quadratic objective function composed of the Lagrangian of the original…

Selective optimization with compensation theory posits that animals optimize their energy intake by adjusting their foraging behavior in response to environmental challenges. When a specific food source is scarce, animals compensate by switching to alternative food sources or adjusting their foraging techniques, maintaining their overall energy intake while minimizing the impact of environmental fluctuations. This…