CVX Example Library

Antenna array design

• Reference: Antenna Array Pattern Synthesis via Convex Optimization

• Reference: FIR Filter Design via Spectral Factorization and Convex Optimization

• Minimize beamwidth of an array with arbitrary 2-D geometry (ant_array_min_beamwidth.m)

• Minimize sidelobe level of a uniform linear array via spectral factorization (line_array_spec_fact.m)

• Minimize sidelobe level of an FIR broadband far-field antenna array (broadband_array_min_sidelobe.m)

• Minimize sidelobe level of an array with arbitrary 2-D geometry (ant_array_min_sidelobe.m)

• Minimize thermal noise power of an array with arbitrary 2-D geometry (ant_array_min_therm_noise.m)

• Utility: Plot a polar plot of an antenna array sensitivity (polar_plot_ant.m)

• Utility: Spectral factorization using Kolmogorov 1939 approach (spectral_fact.m)

Circuit design

• Reference: Optimizing Dominant Time Constant in RC Circuits

• Reference: Optimal Wire and Transistor Sizing for Circuits with Non-Tree Topology

• Reference: Geometric Programming and its Applications to EDA Problems

• Reference: Digital Circuit Optimization via Geometric Programming

• Combined sizing of drivers, repeaters, and wire (wire_driver_sizing.m)

• Combined wire sizing and spacing (wire_sizing_spacing.m)

• Digital circuit sizing example (GP) (dig_ckt_sizing.m)

• Digital circuit sizing for an inverter chain (GP) (inverter_chain_sizing.m)

• Elmore delay sizing for a straight wire (GP) (elmore_straight_wire.m)

• LC oscillator design (GP) (LC_osc_design.m)

• Optimal interconnect wire sizing (wire_sizing.m)

• Sizing of clock meshes (clock_mesh.m)

• Tri-state bus sizing and topology design (tristate_bus_sizing.m)

• Two-input NAND gate sizing (GP) (simple_NAND2_gate_design.m)

• Wire sizing and topology design (wire_sizing_topology.m)

• Utility: Computes the step response of a linear system (simple_step.m)

• Utility: Plots four different taper desings on a single graph. (plot_four_tapers.m)

Figures, examples, and exercises from the book Convex Optimization

• Chapter 4: Convex optimization problems

  • Section 4.3.1: Compute and display the Chebyshev center of a 2D polyhedron (chebyshev_center_2D.m)

  • Section 4.3.1: Compute the Chebyshev center of a polyhedron (chebyshev_center.m)

  • Section 4.5.4: Design of a cantilever beam: recursive formulation (GP) (cantilever_beam_rec.m)

  • Section 4.5.4: Frobenius norm diagonal scaling (GP) (frob_norm_diag_scaling.m)

  • Section 4.5.4: Minimum spectral radius via Peron-Frobenius theory (GP) (min_spec_rad_ppl_dynamics.m)

  • Section 4.6.3: Find the fastest mixing Markov chain on a graph (fastest_mixing_MC.m)

  • Exercise 4.27: Matrix fractional minimization using second-order cone programming (ex_4_27.m)

  • Exercise 4.31: Design of a cantilever beam (GP) (cantilever_beam.m)

  • Exercise 4.38(b): Linear matrix inequalities with one variable (ex_4_38.m)

  • Exercise 4.3: Solve a simple QP with inequality constraints (ex_4_3.m)

  • Exercise 4.47: Maximum determinant PSD matrix completion (max_det_psd_completion.m)

  • Exercise 4.57: Capacity of a communication channel (channel_capacity.m)

  • Exercise 4.5: Show the equivalence of 3 convex problem formations (ex_4_5.m)

  • Exercise 4.60: Log-optimal investment strategy (logopt_investment.m)

  • Utility: Plots a cantilever beam as a 3D figure. (cantilever_beam_plot.m)

• Chapter 5: Duality

  • Section 5.2.4: Solves a simple QCQP (qcqp.m)

  • Section 5.2.5: Mixed strategies for matrix games (matrix_games.m)

  • Section 5.2.5: Mixed strategies for matrix games (LP formulation) (matrix_games_LP.m)

  • Examples 5.6,5.8: An l_p norm approximation problem (norm_approx.m)

  • Exercise 5.19c: Markovitz portfolio optimization w/ diversification constraint (ex_5_19.m)

  • Exercise 5.1d: Sensitivity analysis for a simple QCQP (ex_5_1.m)

  • Exercise 5.33: Parametrized l1-norm approximation (ex_5_33.m)

  • Exercise 5.39: SDP relaxations of the two-way partitioning problem (ex_5_39.m)

• Chapter 6: Approximation and fitting

  • Section 6.1.2: Residual minimization with deadzone penalty (deadzone.m)

  • Figure 6.15: A comparison of stochastic and worst-case robust approximation (fig6_15.m)

  • Figure 6.19: Polynomial fitting (fig6_19.m)

  • Figure 6.24: Fitting a convex function to given data (convex_interpolation.m)

  • Figure 6.2: Penalty function approximation (penalty_comp_cvx.m)

  • Figure 6.9: An optimal tradeoff curve (fig6_9.m)

  • Figures 6.11-6.14: Total variation reconstruction (tv_cvx.m)

  • Figures 6.21-6.23: Basis pursuit using Gabor functions (basispursuit.m)

  • Figures 6.8-6.10: Quadratic smoothing (smoothrec_cvx.m)

  • Example 6.2: Robust regression using the Huber penalty (fig6_5.m)

  • Example 6.3: Optimal input design (fig6_6.m)

  • Example 6.4: Regressor selection problem (regressor_cvx.m)

  • Example 6.6: Comparison of worst-case robust, Tikhonov, and nominal least squares (wcrobls.m)

  • Example 6.8: Spline fitting (fig6_20.m)

  • Example 6.9: Bounding consumer preference (preference_regions.m)

• Chapter 7: Statistical estimation

  • Section 7.1.1: Counting problems with Poisson distribution (counting_problem_poisson.m)

  • Section 7.1.1: Covariance estimation for Gaussian variables (ML_covariance_est.m)

  • Section 7.4.3: Probability bounds example with Voronoi diagram (probbounds.m)

  • Section 7.5.2: Experiment design (expdesign.m)

  • Figure 7.1: Logistic regression (logistics.m)

  • Figure 7.1: Logistic regression (GP version) (logistics_gp.m)

  • Example 7.2: Maximum entropy distribution (maxent.m)

  • Example 7.4: Binary hypothesis testing (detector2.m)

  • Utility: Computes Chebyshev lower bounds on probability vectors (cheb.m)

  • Utility: Computes Chernoff upper bounds on probability (cher.m)

  • Utility: estimates probability than random vector x in R2 (montecarlo.m)

• Chapter 8: Geometric problems

  • Section 8.1.1: Separating a point from a polyhedron (separate_pt_poly.m)

  • Section 8.2.2: Separating polyhedra in 2D (separate_poly_2D.m)

  • Section 8.5.3: Analytic center of a set of linear inequalities (analytic_center.m)

  • Figure 8.10: Approximate linear discrimination via linear programming (svm_1.m)

  • Figure 8.11: Approximate linear discrimination via support vector classifier (svm_2.m)

  • Figure 8.15: Linear placement problem (placement_lin.m)

  • Figure 8.16: Quadratic placement problem (placement_quad.m)

  • Figure 8.17: Fourth-order placement problem (placement_quar.m)

  • Figure 8.8: Simplest linear discrimination (linear_discr.m)

  • Figure 8.9: Robust linear discrimination problem (robust_lin_discr.m)

  • Example 8.3: Bounding correlation coefficients (ex_8_3.m)

  • Example 8.4: One free point localization (ex_8_4.m)

  • Example 8.7: Floorplan generation test script (test_floorplan.m)

  • Euclidean distance between polyhedra (eucl_dist_poly.m)

  • Euclidean distance between polyhedra in 2D (eucl_dist_poly_2D.m)

  • Euclidean projection on a halfspace (eucl_proj_hlf.m)

  • Euclidean projection on a hyperplane (eucl_proj_hyp.m)

  • Euclidean projection on a rectangle (eucl_proj_rect.m)

  • Euclidean projection on the nonnegative orthant (eucl_proj_cone1.m)

  • Euclidean projection on the semidefinite cone (eucl_proj_cone2.m)

  • Floor planning (floor_plan.m)

  • Maximum volume inscribed ellipsoid in a polyhedron (max_vol_ellip_in_polyhedra.m)

  • Minimum volume ellipsoid covering a finite set (min_vol_elp_finite_set.m)

  • Minimum volume ellipsoid covering union of ellipsoids (min_vol_union_ellip.m)

  • One free point localization (ex_8_5.m)

  • Polynomial discrimination (poly3_discr.m)

  • Polynomial discrimination (poly4_discr.m)

  • Quadratic discrimination (separating ellipsoid) (quad_discr.m)

  • Separating ellipsoids in 2D (separate_ell_2D.m)

  • Solve a floor planning problem given graphs H & V (floor_plan_graphs.m)

  • Utility: Computes a minimum-perimeter bounding box subject to positioning constraints (floorplan.m)

  • Data: data_floorplan_32.mat

  • Data: data_floorplan_60.mat

• Chapter 11: Interior-point methods

  • Section 11.8.4: Network rate optimization (log_utility_flow.m)

Filter design

• Reference: FIR Filter Design via Spectral Factorization and Convex Optimization

• Reference: EE364 lecture, Filter design and equalization

• Chebychev design of an FIR filter given a desired H(w) (fir_chebychev_design.m)

• Design a 1/f spectrum shaping (pink-noise) filter (one_over_f_filter.m)

• Equalizer design example (equalizer_design.m)

• Maximize stopband attenuation of a bandpass IIR filter (iir_mag_design_bandpass_max_atten.m)

• Maximize stopband attenuation of a linear phase lowpass FIR filter (fir_lin_phase_lowpass_max_atten.m)

• Maximize stopband attenuation of a lowpass FIR filter (magnitude design) (fir_mag_design_lowpass_max_atten.m)

• Maximize stopband attenuation of a lowpass IIR filter (iir_mag_design_lowpass_max_atten.m)

• Minimize order of a linear phase lowpass FIR filter (fir_lin_phase_lowpass_min_order.m)

• Minimize order of a lowpass FIR filter (magnitude design) (fir_mag_design_lowpass_min_order.m)

• Minimize stopband ripple of a linear phase lowpass FIR filter (fir_lin_phase_lowpass_min_ripple.m)

• Minimize transition bandwidth of a linear phase lowpass FIR filter (fir_lin_phase_lowpass_min_trans.m)

• Utility: Spectral factorization using Kolmogorov 1939 approach. (spectral_fact.m)

Examples from A Tutorial on Geometric Programming

• Box volume maximization (max_volume_box.m)

• Digital circuit sizing (simple_dig_ckt_sizing.m)

• Digital circuit sizing (vectorized) (simple_dig_ckt_sizing_vect.m)

• Elmore delay sizing for an interconnect network. (elmore_interconnect.m)

• Floor planning with an optimal trade-off curve. (floor_planning.m)

• Optimal doping profile optimization (basic_odp.m)

• Optimal doping profile optimization with current gain constraint. (beta_min_odp.m)

• Simple power control in communication systems via GP. (power_control.m)

Graph Laplacian eigenvalue optimization

• Reference: Convex Optimization of Graph Laplacian Eigenvalues

• FDLA and FMMC solutions for a 50-node, 200-edge graph (larger_example.m)

• FDLA and FMMC solutions for a 64-node, 95-edge cut-grid graph (cut_grid_example.m)

• FDLA and FMMC solutions for an 8-node, 13-edge graph (small_example.m)

• Utility: Computes fastest mixing Markov chain (FMMC) edge weights (fmmc.m)

• Utility: Computes the Metropolis-Hastings heuristic edge weights (mh.m)

• Utility: Computes the constant edge weight that yields fastest averaging. (best_const.m)

• Utility: Computes the fastest distributed linear averaging (FDLA) edge weights (fdla.m)

• Utility: Computes the maximum-degree heuristic edge weights (max_deg.m)

• Utility: Generate a cut-grid graph for the ICM 2006 talk example (cut_grid_data.m)

• Utility: Plots a graph with each edge width proportional to its weight. (plotgraph.m)

Examples employing logarithms, exponentials, and entropy functions

• Entropy maximization (max_entropy.m)

• Sparse covariance estimation for Gaussian variables (sparse_covariance_est.m)

• Sparse covariance estimation for Gaussian variables (sparse_covariance_est_tradeoff.m)

• Weighted analytic center of a set of linear inequalities (weighted_analytic_center.m)

Sparse solution heuristics

• Computing a sparse solution of a set of linear inequalities (sparse_solution.m)

• Detecting a small subset of infeasible linear inequalities (sparse_infeas_dual.m)

• Finding a point that satisfies many linear inequalities (sparse_infeas.m)

Example from Trend Filtering

• l1 trend filtering (l1_trend_filter_snp500.m)

• Data: snp500.txt

Miscellaneous examples

• Examples from the CVX User's guide (quickstart.m)

• Builds a norm minimization tradeoff curve (regularized_norm_tradeoff.m)

• Builds and solves a simple inequality-constrained linear program (simple_LP2.m)

• Builds and solves a simple least-squares problem using cvx (simple_LS.m)

• Builds and solves a simple linear program (simple_LP.m)

• Closest Toeplitz SDP search. (closest_toeplitz_psd.m)

• Equality constrained norm minimization. (equality_constr_norm_min.m)

• Minimal phase spectral factorization (min_phase_spectral_fact.m)

• Nonnegative matrix factorization (nonneg_matrix_fact.m)