{wiki=José_de_Jesús_Martínez}

José de Jesús Martínez can refer to various individuals, but without more context, it's hard to determine which specific person you're asking about. It could be a common name in Spanish-speaking countries.


José de Jesús Martínez

{wiki=Penalty_method}

The Penalty Method is a mathematical technique commonly used in optimization problems, particularly in nonlinear programming. It involves adding a penalty term to the objective function to discourage violation of constraints. This method enables the transformation of a constrained optimization problem into an unconstrained one. \#\#\# Key Components of the Penalty Method: 1. **Objective Function**: The original function you want to optimize (minimize or maximize).


Penalty method

{wiki=Powell's_dog_leg_method}

Powell's dog leg method is an iterative algorithm used for solving nonlinear optimization problems, particularly suitable for problems with least-squares formulations. It is commonly employed in the context of finding the minimum of a scalar function that is expressed as the sum of squares of functions. This method is particularly useful when dealing with functions that are not easily differentiable or when derivatives are difficult to compute. The dog leg method combines two approaches: the gradient descent method and the Gauss-Newton method.


Powell's dog leg method

{wiki=Quadratic_programming}

Quadratic programming (QP) is a type of mathematical optimization problem that involves a quadratic objective function and linear constraints. It is a special case of mathematical programming that is particularly useful in various fields, including operations research, finance, engineering, and machine learning. \#\#\# Key Components of Quadratic Programming 1.


Quadratic programming

{wiki=Quantum_annealing}

Quantum annealing is a quantum computing technique used to solve optimization problems. It leverages the principles of quantum mechanics, particularly quantum superposition and quantum tunneling, to find the global minimum of a given objective function more efficiently than classical methods. Here are some key points about quantum annealing: 1. **Optimization Problems**: Quantum annealing is particularly useful for problems where the goal is to minimize or maximize a cost function, often framed as finding the best configuration of a system among many possibilities.


Quantum annealing

{wiki=Random_search}

Random search is a simple optimization technique often used in hyperparameter tuning and other types of search problems. Instead of systematically exploring the parameter space (as in grid search), random search samples parameters randomly from a designated space. Here's a breakdown of its key features and advantages: \#\#\# Key Features 1. **Sampling**: In random search, you define a range or distribution for each parameter and sample values randomly from these distributions to evaluate the performance of a model.


Random search

{wiki=Robust_fuzzy_programming}

Robust fuzzy programming is a type of optimization approach that incorporates both fuzzy logic and robustness into decision-making processes, particularly in the face of uncertainty. It combines the principles of fuzzy set theory—in which uncertainty and imprecision are modeled linguistically—and robust optimization, which focuses on finding solutions that remain effective under a variety of uncertain future scenarios.


Robust fuzzy programming

{wiki=Ruzzo–Tompa_algorithm}

The Ruzzo–Tompa algorithm is a method for efficiently determining whether a given string contains a specific substring. This algorithm is particularly useful in the context of pattern matching in strings, specifically when the substring is short compared to the text, or when speed is of primary concern. Developed by Giuseppe Ruzzo and Daniel Tompa, the algorithm leverages techniques from theoretical computer science, particularly those surrounding deterministic finite automata (DFA) and regular expressions.


Ruzzo–Tompa algorithm

{wiki=Search-based_software_engineering}

Search-Based Software Engineering (SBSE) is an approach within the field of software engineering that applies search-based optimization techniques to various software engineering problems. The fundamental idea is to model software development challenges as optimization problems that can be tackled using search algorithms, often inspired by natural processes such as evolution (e.g., genetic algorithms), swarm intelligence, or other heuristic methods. \#\#\# Key Concepts 1.


Search-based software engineering

{wiki=Sequential_linear-quadratic_programming}

Sequential Linear-Quadratic Programming (SLQP) is an optimization technique primarily used for solving nonlinear programming problems with specific structure. It combines elements of linear programming and quadratic programming, allowing for the efficient resolution of complex optimization problems that involve nonlinear constraints and objective functions. The method works by iteratively approximating the nonlinear problem with a series of linear programming or quadratic programming problems.


Sequential linear-quadratic programming

{wiki=Simplex_algorithm}

The Simplex algorithm is a widely used method for solving linear programming problems, which are mathematical optimization problems where the objective is to maximize or minimize a linear function subject to a set of linear constraints. Developed by George Dantzig in the 1940s, the Simplex algorithm efficiently finds the optimal solution by moving along the edges of the feasible region defined by the constraints.


Simplex algorithm

{wiki=Zionts–Wallenius_method}

The Zionts–Wallenius method is a mathematical approach used primarily in the context of decision-making, particularly in multi-criteria decision analysis (MCDA). Developed by Aaron Zionts and Delbert Wallenius, this method focuses on providing a systematic way to evaluate and rank alternatives based on multiple, possibly conflicting criteria.


Zionts–Wallenius method

{wiki=Simulated_annealing}

Simulated annealing is a probabilistic optimization algorithm inspired by the annealing process in metallurgy, where controlled cooling of materials leads to a more stable crystal structure. It is used to find an approximate solution to optimization problems, especially those that are discrete or combinatorial in nature. \#\#\# Key Concepts: 1. **Metaphor of Annealing**: In metallurgy, when a metal is heated and then gradually cooled, it allows the atoms to settle into a more organized and low-energy state.


Simulated annealing

{wiki=Space_allocation_problem}

The space allocation problem typically refers to the challenge of efficiently allocating limited resources, such as space, to various tasks or items in a way that optimizes a specific objective. While the term can be applied in different contexts, it commonly appears in fields like operations research, computer science, urban planning, and logistics.


Space allocation problem

{wiki=Special_ordered_set}

A **special ordered set**, often abbreviated as SOS, is a specific type of set used primarily in combinatorial optimization and various mathematical programming contexts. The key feature of an SOS is that it imposes certain restrictions on the elements of the set, typically in integer programming scenarios.


Special ordered set

{wiki=Spiral_optimization_algorithm}

The Spiral Optimization Algorithm (SOA) is a relatively recent algorithm inspired by the natural processes of spirals found in various phenomena, such as the arrangement of seeds in a sunflower or the shape of galaxies. It is a part of a broader category of bio-inspired algorithms, which also includes methods like genetic algorithms, particle swarm optimization, and ant colony optimization. \#\#\# Key Features of the Spiral Optimization Algorithm 1.


Spiral optimization algorithm

{wiki=Stochastic_dynamic_programming}

Stochastic dynamic programming (SDP) is an extension of dynamic programming that incorporates randomness in decision-making processes. It is a mathematical method used to solve problems where decisions need to be made sequentially over time in the presence of uncertainty. \#\#\# Key Components of Stochastic Dynamic Programming: 1. **State Space**: The set of all possible states that the system can be in. A state captures all relevant information necessary to make decisions at any point in the process.


Stochastic dynamic programming

{wiki=Stochastic_programming}

Stochastic programming is a framework for modeling optimization problems that involve uncertainty. Unlike traditional deterministic optimization, where the parameters of the model (such as costs, demands, or resource availabilities) are known with certainty, stochastic programming accounts for uncertainty by incorporating random variables and probabilistic constraints. The main idea is to make decisions that are robust against various possible future scenarios, allowing decision-makers to optimize an objective function while taking into consideration the risks and uncertainties inherent in the problem.


Stochastic programming

{wiki=Successive_linear_programming}

Successive linear programming (SLP) is an iterative optimization technique used to solve nonlinear programming problems by breaking them down into a series of linear programming problems. The basic idea is to linearize a nonlinear objective function or constraints around a current solution point, solve the resulting linear programming problem, and then update the solution based on the results. Here’s how it generally works: 1. **Initial Guess**: Start with an initial guess for the variables.


Successive linear programming

{wiki=Ternary_search}

Ternary search is a divide-and-conquer search algorithm that is used to find the maximum or minimum value of a unimodal function. A unimodal function is defined as one that has a single local maximum or minimum within a given interval. Ternary search divides the search interval into three parts, which results in two midpoints, and then eliminates one of the three segments based on the comparison of the function values at these midpoints.


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