Projects in Awesome Lists tagged with optimization-algorithms

https://github.com/jason2brownlee/cleveralgorithms

Clever Algorithms: Nature-Inspired Programming Recipes

algorithms book computational-intelligence machine-learning-algorithms optimization-algorithms

Last synced: 14 May 2025

https://github.com/jbrownlee/CleverAlgorithms

Clever Algorithms: Nature-Inspired Programming Recipes

algorithms book computational-intelligence machine-learning-algorithms optimization-algorithms

Last synced: 22 Feb 2025

https://github.com/ljvmiranda921/pyswarms

A research toolkit for particle swarm optimization in Python

algorithm discrete-optimization global-optimization machine-learning metaheuristics optimization optimization-algorithms optimization-tools particle-swarm-optimization pso swarm-intelligence

Last synced: 14 May 2025

https://github.com/timefoldai/timefold-solver

The open source Solver AI for Java, Python and Kotlin to optimize scheduling and routing. Solve the vehicle routing problem, employee rostering, task assignment, maintenance scheduling and other planning problems.

ai artificial-intelligence constraint-programming constraint-solver cvrp employee-scheduling java kotlin maintenance-scheduling operations-research optimization-algorithms planning-algorithms python resource-allocation solver solver-library vehicle-routing vehicle-routing-problem vrp vrptw

Last synced: 13 May 2025

https://github.com/captain1986/captainblackboard

船长关于机器学习、计算机视觉和工程技术的总结和分享

computer-vision convolutional-neural-networks deep-learning optimization-algorithms summary

Last synced: 16 May 2025

https://github.com/cvxgrp/cvxportfolio

Portfolio optimization and back-testing.

convex-optimization finance optimization optimization-algorithms optimization-methods optimizer portfolio-optimization python time-series

Last synced: 14 May 2025

https://github.com/argmin-rs/argmin

Numerical optimization in pure Rust

numerical-optimization optimization optimization-algorithms optimization-methods optimizer rust

Last synced: 20 Mar 2025

https://github.com/TimefoldAI/timefold-solver

The open source Solver AI for Java, Python and Kotlin to optimize scheduling and routing. Solve the vehicle routing problem, employee rostering, task assignment, maintenance scheduling and other planning problems.

ai artificial-intelligence constraint-programming constraint-solver cvrp employee-scheduling java kotlin maintenance-scheduling operations-research optimization-algorithms planning-algorithms python resource-allocation solver solver-library vehicle-routing vehicle-routing-problem vrp vrptw

Last synced: 05 Apr 2025

https://github.com/nnaisense/evotorch

Advanced evolutionary computation library built directly on top of PyTorch, created at NNAISENSE.

artificial-intelligence distributed evolutionary-algorithms evolutionary-computation gpu neural-networks neuroevolution optimization optimization-algorithms python pytorch reinforcement-learning

Last synced: 05 Apr 2025

https://github.com/patwie/cppnumericalsolvers

a lightweight header-only C++17 library of numerical optimization methods for nonlinear functions based on Eigen

bfgs cpp11 eigen gradient-computation lbfgs lbfgs-solver lbfgsb-solver mathematics minimization minimization-algorithm newton numerical-optimization-methods optim optimisation optimization optimization-algorithms optimization-tools solver solvers

Last synced: 16 May 2025

https://github.com/PatWie/CppNumericalSolvers

a lightweight header-only C++17 library of numerical optimization methods for nonlinear functions based on Eigen

bfgs cpp11 eigen gradient-computation lbfgs lbfgs-solver lbfgsb-solver mathematics minimization minimization-algorithm newton numerical-optimization-methods optim optimisation optimization optimization-algorithms optimization-tools solver solvers

Last synced: 15 Mar 2025

https://github.com/kthohr/optim

OptimLib: a lightweight C++ library of numerical optimization methods for nonlinear functions

armadillo automatic-differentiation bfgs cpp cpp11 differential-evolution eigen eigen3 evolutionary-algorithms gradient-descent lbfgs newton numerical-optimization-methods openmp openmp-parallelization optim optimization optimization-algorithms particle-swarm-optimization

Last synced: 16 May 2025

https://github.com/esa/pagmo2

A C++ platform to perform parallel computations of optimisation tasks (global and local) via the asynchronous generalized island model.

artificial-intelligence evolutionary-algorithms evolutionary-strategy genetic-algorithm metaheuristics multi-objective-optimization optimization optimization-algorithms optimization-methods optimization-tools pagmo parallel-computing parallel-processing python python3 stochastic-optimizers

Last synced: 15 May 2025

https://github.com/mlpack/ensmallen

A header-only C++ library for numerical optimization --

deep-learning function-optimization machine-learning minimization optimization optimization-algorithms

Last synced: 14 May 2025

https://github.com/cerndb/dist-keras

Distributed Deep Learning, with a focus on distributed training, using Keras and Apache Spark.

apache-spark data-parallelism data-science deep-learning distributed-optimizers hadoop keras machine-learning optimization-algorithms tensorflow

Last synced: 22 Jan 2025

https://github.com/ArashPartow/exprtk

C++ Mathematical Expression Parsing And Evaluation Library https://www.partow.net/programming/exprtk/index.html

ast c-plus-plus compiler expression-evaluator expression-parser exprtk grammar high-performance language lexer math math-expressions mathematics mirrored-repository mit-license numerical-calculations optimization-algorithms parser scientific-computing semantic-analyzer

Last synced: 15 Mar 2025

https://github.com/100/Solid

🎯 A comprehensive gradient-free optimization framework written in Python

algorithm artificial-intelligence continuous-optimization discrete-optimization evolutionary-algorithm genetic-algorithm genetic-algorithm-framework harmony-search hill-climbing library machine-learning machine-learning-algorithms metaheuristics optimization optimization-algorithms particle-swarm-optimization python simulated-annealing stochastic-optimizers tabu-search

Last synced: 27 Nov 2024

https://github.com/100/solid

🎯 A comprehensive gradient-free optimization framework written in Python

algorithm artificial-intelligence continuous-optimization discrete-optimization evolutionary-algorithm genetic-algorithm genetic-algorithm-framework harmony-search hill-climbing library machine-learning machine-learning-algorithms metaheuristics optimization optimization-algorithms particle-swarm-optimization python simulated-annealing stochastic-optimizers tabu-search

Last synced: 04 Apr 2025

https://github.com/cvxgrp/scs

Splitting Conic Solver

cone-programming convex-optimization first-order-methods linear-programming numerical-optimization optimization optimization-algorithms quadratic-programming semidefinite-programming solver

Last synced: 16 May 2025

https://github.com/coin-or/python-mip

Python-MIP: collection of Python tools for the modeling and solution of Mixed-Integer Linear programs

integer-programming linear-programming mip modeling optimization optimization-algorithms optimization-framework optimization-tools

Last synced: 19 Jun 2025

https://github.com/haaleo/swarmlib

This repository implements several swarm optimization algorithms and visualizes them. Implemented algorithms: Particle Swarm Optimization (PSO), Firefly Algorithm (FA), Cuckoo Search (CS), Ant Colony Optimization (ACO), Artificial Bee Colony (ABC), Grey Wolf Optimizer (GWO) and Whale Optimization Algorithm (WOA)

aco ant-colony-optimization artificial-bee-colony cuckoo-search firefly-algorithm grey-wolf-optimizer gwo heuristic-optimization heuristic-search-algorithms levy-walks optimization-algorithms particle-swarm-optimization pso pypi swarm traveling-salesman-problem tsp tsplib tsplib95 whale-optimization

Last synced: 12 Apr 2025

https://github.com/esa/pygmo2

A Python platform to perform parallel computations of optimisation tasks (global and local) via the asynchronous generalized island model.

artificial-intelligence evolutionary-algorithms evolutionary-computation evolutionary-strategy island-model meta-heuristic meta-heuristics multiobjective-optimization optimization optimization-algorithms optimization-methods optimization-problem parallel-computing parallel-processing stochastic-optimization

Last synced: 16 May 2025

https://github.com/j-w-yun/optimizer-visualization

Visualize Tensorflow's optimizers.

adamoptimizer gradientdescentoptimizer learning-rate machine-learning optimization-algorithms optimizer-visualization tensorflow

Last synced: 09 Apr 2025

https://github.com/yuanhaogong/curvaturefilter

Curvature Filters are efficient solvers for Variational Models

curvature curvature-filters differential-geometry image-processing itk matlab opencv optimization-algorithms python

Last synced: 06 Apr 2025

https://github.com/YuanhaoGong/CurvatureFilter

Curvature Filters are efficient solvers for Variational Models

curvature curvature-filters differential-geometry image-processing itk matlab opencv optimization-algorithms python

Last synced: 15 Mar 2025

https://github.com/benfred/fmin

Unconstrained function minimization in Javascript

numerical-optimization optimization-algorithms visualization

Last synced: 14 May 2025

https://github.com/star2dust/paper-simulation

Let's reproduce paper simulations of multi-robot systems, formation control, distributed optimization and cooperative manipulation.

cooperative-manipulation formation-control matlab multi-agent-systems multi-robot-cooperation optimization-algorithms paper-simulations robotics

Last synced: 06 Apr 2025

https://github.com/apache/incubator-kie-optaplanner-quickstarts

OptaPlanner quick starts for AI optimization: many use cases shown in many different technologies.

artificial-intelligence constraint-solver gradle java kotlin mathematical-optimization maven operations-research optimization-algorithms quarkus solver spring-boot

Last synced: 15 May 2025

https://github.com/cvanaret/uno

A next-gen SQP & barrier solver for nonlinearly constrained optimization

constrained-optimization continuous-optimization cpp gradient-descent interior-point-method local-optimization mathematical-optimization mathematical-programming newton-method nonconvex-optimization nonlinear-optimization nonlinear-programming nonlinear-programming-algorithms numerical-optimization optimization optimization-algorithms optimization-methods optimization-solver quadratic-programming sequential-quadratic-programming

Last synced: 16 May 2025

https://github.com/imagry/aleph_star

Reinforcement learning with A* and a deep heuristic

control-systems dqn machine-learning-algorithms optimization-algorithms reinforcement-learning reinforcement-learning-algorithms shortest-path

Last synced: 27 Nov 2024

https://github.com/nvidia/cuopt-resources

A collection of NVIDIA cuOpt samples and other resources

cvrp cvrptw gpu gpu-acceleration gpu-optimization intralogistics last-mile-delivery logistics nvidia-gpu operations-research optimization optimization-algorithms optimization-tools pickup-and-delivery route-optimization traveling-salesman-problem tsp-solver vehicle-routing-problem vrp vrp-solver

Last synced: 04 Apr 2025

https://github.com/bwohlberg/sporco

Sparse Optimisation Research Code

admm convolutional-dictionary-learning convolutional-sparse-coding cuda dictionary-learning fista optimization optimization-algorithms plug-and-play-priors python robust-pca sparse-coding sparse-representations sparsity total-variation total-variation-minimization

Last synced: 15 May 2025

https://github.com/gitabcworld/FewShotLearning

Pytorch implementation of the paper "Optimization as a Model for Few-Shot Learning"

few-shot optimization optimization-algorithms python pytorch

Last synced: 08 May 2025

https://github.com/tim-salzmann/l4casadi

Use PyTorch Models with CasADi and Acados in Python, C(++) or Matlab

acados casadi cplusplus deep-learning learning-control machine-learning optimization optimization-algorithms python pytorch

Last synced: 05 Apr 2025

https://github.com/acerbilab/bads

Bayesian Adaptive Direct Search (BADS) optimization algorithm for model fitting in MATLAB

bayesian-optimization log-likelihood matlab noiseless-functions noisy-functions optimization-algorithms

Last synced: 09 Apr 2025

https://github.com/lanl-ansi/alpine.jl

A Julia/JuMP-based Global Optimization Solver for Non-convex Programs

global-optimization julia-language minlp minlp-solver mixed-integer-nonlinear-programming mixed-integer-programming non-convex-optimization nonlinear-optimization optimization optimization-algorithms

Last synced: 15 May 2025

https://github.com/jaswinder9051998/zoofs

zoofs is a python library for performing feature selection using a variety of nature-inspired wrapper algorithms. The algorithms range from swarm-intelligence to physics-based to Evolutionary. It's easy to use , flexible and powerful tool to reduce your feature size.

evolutionary-algorithms feature-selection genetic-algorithm grey-wolf grey-wolf-optimizer machine-learning machine-learning-algorithms machinelearning optimization optimization-algorithms optimization-methods optimization-tools particle-swarm particle-swarm-optimization python subset-selection supervised-learning

Last synced: 01 May 2025

https://github.com/oxfordcontrol/clarabel.rs

Clarabel.rs: Interior-point solver for convex conic optimisation problems in Rust.

conic-optimization conic-programs convex-optimization interior-point-method linear-programming optimization optimization-algorithms quadratic-programming rust-lang semidefinite-programming

Last synced: 09 Apr 2025

https://github.com/idaholab/raven

RAVEN is a flexible and multi-purpose probabilistic risk analysis, validation and uncertainty quantification, parameter optimization, model reduction and data knowledge-discovering framework.

data-mining model-calibration model-reduction optimization-algorithms parametric-analysis probabilistic-analysis risk-analysis uncertainty-quantification validation

Last synced: 08 Apr 2025

https://github.com/albarji/proxtv

Matlab and Python toolbox for fast Total Variation proximity operators

machine-learning optimization-algorithms proximal-operators signal-processing

Last synced: 06 Apr 2025

https://github.com/oxfordcontrol/clarabel.jl

Clarabel.jl: Interior-point solver for convex conic optimisation problems in Julia.

conic-optimization conic-programs convex-optimization interior-point-method julia-language linear-programming optimization optimization-algorithms quadratic-programming semidefinite-programming

Last synced: 16 May 2025

https://github.com/Evolutionary-Intelligence/pypop

[JMLR-2024] PyPop7: A Pure-Python Library for POPulation-based Black-Box Optimization (BBO), especially their *Large-Scale* versions/variants (evolutionary algorithms/swarm-based optimizers/pattern search/...).

black-box-optimization consensus-based-optimization continuous-optimization derivative-free-optimization differential-evolution direct-search estimation-of-distribution-algorithms evolution-strategies evolutionary-algorithms genetic-algorithms global-optimization gradient-free-optimization large-scale-optimization nonlinear-optimization numerical-optimization optimization-algorithms particle-swarm-optimization population-based-optimization random-search zeroth-order-optimization

Last synced: 26 Feb 2025

https://github.com/innoave/genevo

Execute genetic algorithm (GA) simulations in a customizable and extensible way.

evolutionary-algorithms framework genetic-algorithm library optimization-algorithms rust search-algorithms

Last synced: 04 Apr 2025

https://github.com/hybridrobotics/car-racing

A toolkit for testing control and planning algorithm for car racing.

car-racing casadi control-barrier-functions learning model-predictive-control nonlinear-optimization obstacle-avoidance optimization-algorithms simulation trajectory-optimization

Last synced: 17 Mar 2025

https://github.com/lacerbi/optimviz

Visualize optimization algorithms in MATLAB.

matlab optimization optimization-algorithms visualization

Last synced: 14 Apr 2025

https://github.com/emadehsan/csp

Algorithm for Cutting Stock Problem using Google OR-Tools. Link to the tool:

cutting-stock cutting-stock-problem google operations-research optimization optimization-algorithms ortools python

Last synced: 01 May 2025

https://github.com/juliafirstorder/proximalalgorithms.jl

Proximal algorithms for nonsmooth optimization in Julia

admm julia machine-learning nonlinear-programming nonsmooth-optimization numerical-optimization optimal-control optimization optimization-algorithms proximal-algorithms proximal-gradient-method proximal-operators

Last synced: 04 Apr 2025

https://github.com/ciren/cilib

Typesafe, purely functional Computational Intelligence

cilib computational-intelligence functional-programming machine-learning optimization-algorithms scala

Last synced: 27 Mar 2025

https://github.com/cirg-up/cilib

Typesafe, purely functional Computational Intelligence

cilib computational-intelligence functional-programming machine-learning optimization-algorithms scala

Last synced: 29 Nov 2024

https://github.com/soypat/mu8

Genetic algorithm for unsupervised machine learning in Go.

algorithm evolutionary-algorithm genetic-algorithm genetic-algorithms go go-generics golang golang-generics island-model machine-learning optimization optimization-algorithms unsupervised-machine-learning

Last synced: 16 Mar 2025

https://github.com/jefffessler/mirt.jl

MIRT: Michigan Image Reconstruction Toolbox (Julia version)

image-reconstruction inverse-problems julia k-space lasso mirt mri nufft optimization-algorithms sinogram sparse-coding tomography

Last synced: 04 Apr 2025

https://github.com/theochem/procrustes

Python library for finding the optimal transformation(s) that makes two matrices as close as possible to each other.

chemical-structure-similarity generalized-procrustes-analysis generalized-procrustes-problem gpa matrix-transformations molecular-alignment optimization optimization-algorithms orthogonal-procrustes-problem permutation-procrustes-problem procrustes procrustes-analysis quadratic-assignment-problem rotational-procrustes-problem softassign-method symmetric-procrustes-problem

Last synced: 07 Apr 2025

https://github.com/wassname/viz_torch_optim

Videos of deep learning optimizers moving on 3D problem-landscapes

3d-graphics deep-learning learning-rate machine-learning optimization-algorithms optimizer pytorch vizualisation

Last synced: 28 Jan 2025

https://github.com/pdfo/pdfo

Powell's Derivative-Free Optimization solvers.

blackbox-optimization bobyqa cobyla constrained-optimization derivative-free-optimization fortran lincoa matlab newuoa nonlinear-optimization numerical-optimization optimization optimization-algorithms powell python simulation simulation-based-optimization unconstrained-optimization uobyqa zeroth-order-optimization

Last synced: 16 May 2025

https://github.com/nojhan/paradiseo

An evolutionary computation framework to (automatically) build fast parallel stochastic optimization solvers

algorithm cpp cpp17 evolutionary-algorithm framework metaheuristics optimization optimization-algorithms paradiseo parallelization search-heuristics solvers

Last synced: 04 Apr 2025

https://github.com/zib-iol/frankwolfe.jl

Julia implementation for various Frank-Wolfe and Conditional Gradient variants

conditional-gradients first-order-methods frank-wolfe hacktoberfest julia optimization optimization-algorithms

Last synced: 04 Apr 2025

https://github.com/bentrevett/a-tour-of-pytorch-optimizers

A tour of different optimization algorithms in PyTorch.

adadelta adagrad adam optimization optimization-algorithms pytorch pytorch-optimizers rmsprop sgd

Last synced: 10 Apr 2025

https://github.com/control-toolbox/optimalcontrol.jl

Model and solve optimal control problems in Julia

control-systems differentiable-programming differential-geometry geometry julia nonlinear-equations numerical-methods optimal-control optimization optimization-algorithms ordinary-differential-equations quantum-optimal-control

Last synced: 05 Apr 2025

https://github.com/maxim5/hyper-engine

Python library for Bayesian hyper-parameters optimization

bayesian-optimization big-data convolutional-neural-networks data-science deep-learning gaussian-processes hyperparameter-optimization machine-learning model-selection neural-network optimization-algorithms python random-search tensorflow

Last synced: 06 Apr 2025

https://github.com/torressa/cspy

A collection of algorithms for the (Resource) Constrained Shortest Path problem in Python / C++ / C#

bidirectional-labeling-algorithm csp-problem operations-research optimization optimization-algorithms optimization-library resource-constrained-shortest-path

Last synced: 07 Apr 2025

https://github.com/google-research/jestimator

Amos optimizer with JEstimator lib.

deep-learning flax jax language-model machine-learning mnist optimization optimization-algorithms optimizer transformer

Last synced: 20 Dec 2024

https://github.com/lanl/pyharmonysearch

pyHarmonySearch is a pure Python implementation of the harmony search (HS) global optimization algorithm.

applied-mathematics harmony-search heuristic-search-algorithms optimization-algorithms python

Last synced: 19 Dec 2024

https://github.com/LuXDAmore/nuxt-prune-html

🔌⚡ Nuxt module to prune html before sending it to the browser (it removes elements matching CSS selector(s)), useful for boosting performance showing a different HTML for bots/audits by removing all the scripts with dynamic rendering

audit bot cheerio dynamic-rendering html lighthouse measure modules nuxt nuxt-module nuxtjs optimization optimization-algorithms optimize pagespeed-insights performance prune pruning vuejs web-vitals

Last synced: 30 Mar 2025

https://github.com/luxdamore/nuxt-prune-html

🔌⚡ Nuxt module to prune html before sending it to the browser (it removes elements matching CSS selector(s)), useful for boosting performance showing a different HTML for bots/audits by removing all the scripts with dynamic rendering

audit bot cheerio dynamic-rendering html lighthouse measure modules nuxt nuxt-module nuxtjs optimization optimization-algorithms optimize pagespeed-insights performance prune pruning vuejs web-vitals

Last synced: 07 May 2025

https://github.com/coin-or/minotaur

Minotaur Toolkit for Mixed-Integer Nonlinear Optimization

combinatorial-optimization integer-optimization mixed-integer-programming nonlinear-optimization open-source optimization-algorithms

Last synced: 19 Jun 2025

https://github.com/juliafirstorder/structuredoptimization.jl

Structured optimization in Julia

convex-optimization large-scale non-convex non-smooth optimization-algorithms

Last synced: 24 Feb 2025

https://github.com/ghackebeil/pybnb

A parallel branch-and-bound engine for Python. (https://pybnb.readthedocs.io/)

branch-and-bound optimization optimization-algorithms python

Last synced: 14 Apr 2025

https://github.com/diogomatoschaves/geneal

A genetic algorithm implementation in python

genetic-algorithm genetic-programming optimization optimization-algorithms python travelling-salesman-problem

Last synced: 15 Apr 2025

https://github.com/mlopez-ibanez/irace

Iterated Racing for Automatic Algorithm Configuration

algorithm-configuration hyperparameter-tuning irace optimization-algorithms r r-package

Last synced: 13 Apr 2025

https://github.com/jutho/optimkit.jl

OptimKit: A blissfully ignorant Julia package for gradient optimization

conjugate-gradient gradient-optimization l-bfgs optimization optimization-algorithms

Last synced: 18 Feb 2025

https://github.com/srom/cma-es

Covariance Matrix Adaptation Evolution Strategy (CMA-ES)

numerical-optimization optimization optimization-algorithms python tensorflow

Last synced: 02 May 2025

https://github.com/team-approx-bayes/ivon

IVON optimizer for neural networks based on variational learning.

deep-learning optimization-algorithms optimizer python pytorch variational-inference

Last synced: 09 Apr 2025

https://github.com/ahmedfgad/gari

GARI (Genetic Algorithm for Reproducing Images) reproduces a single image using Genetic Algorithm (GA) by evolving pixel values.

evolutionary-algorithms genetic-algorithm genetic-analysis image-analysis image-manipulation image-processing image-reproduction optimization-algorithms python python3

Last synced: 23 Apr 2025

https://github.com/firefly-cpp/fireflyalgorithm

Implementation of Firefly Algorithm in Python

firefly-algorithm optimization optimization-algorithms swarm-intelligence

Last synced: 05 Apr 2025

https://github.com/acerbilab/pybads

PyBADS: Bayesian Adaptive Direct Search optimization algorithm for model fitting in Python

bayesian-optimization log-likelihood noiseless-functions noisy-functions optimization-algorithms python

Last synced: 22 Nov 2024

https://github.com/fpicetti/occamypy

Python library for solving large-scale inverse problems

cluster-computing multiscale optimization optimization-algorithm-library optimization-algorithms

Last synced: 07 May 2025

https://github.com/ccssmnn/hego

Metaheuristics / Blackbox Optimization Algorithms for Go: Simulated Annealing, Genetic Algorithm, Ant Colony Optimization, Tabu Search, Particle Swarm Optimization ...

ant-colony-optimization evolutionary-algorithm genetic-algorithm go optimization optimization-algorithms particle-swarm-optimization simulated-annealing tabu-search

Last synced: 10 Apr 2025

https://github.com/thyeem/monotree

An optimized Sparse Merkle Tree in Rust

cryptocurrency database inclusion-proof optimization-algorithms rust sparse-merkle-tree

Last synced: 17 Jun 2025

https://github.com/Ivan-Zhou/Uber_Driver_Schedule_Optimization

A predictive model to help Uber drivers make more money

geographic-data mip mixed-integer-programming optimization optimization-algorithms schedule taxi taxi-data uber-data uber-drivers

Last synced: 27 Nov 2024

https://github.com/krichelj/pydiffgame

PyDiffGame is a Python implementation of a Nash Equilibrium solution to Differential Games, based on a reduction of Game Hamilton-Bellman-Jacobi (GHJB) equations to Game Algebraic and Differential Riccati equations, associated with Multi-Objective Dynamical Control Systems

artificial-intelligence-algorithms bellman-equation computer-science control-theory differential-equations differential-game dynamical-systems game-theory hamilton-jacobi-bellman hamiltonian inverted-pendulum matrix-equations multi-objective-optimization nash-equilibrium numerical-methods object-oriented-programming optimization-algorithms pontryagin-maximum-principle quadrotor riccati-equation